Econ101L HW11

Solution Key

1. (30 points in total)

Q / Demand / MC / MEC / MSC / MC+tax
0 / 1920 / 800 / 0 / 800 / 1120
10 / 1820 / 860 / 64 / 924 / 1180
20 / 1720 / 920 / 128 / 1048 / 1240
30 / 1620 / 980 / 192 / 1172 / 1300
40 / 1520 / 1040 / 256 / 1296 / 1360
50 / 1420 / 1100 / 320 / 1420 / 1420
60 / 1320 / 1160 / 384 / 1544 / 1480
70 / 1220 / 1220 / 448 / 1668 / 1540
80 / 1120 / 1280 / 512 / 1792 / 1600
90 / 1020 / 1340 / 576 / 1916 / 1660
100 / 920 / 1400 / 640 / 2040 / 1720

.Complete the P (demand) and MC of following table. ( each column 2 points)

  1. What are the market equilibrium price and quantity?

P*=1220 Q*=70 (3 points)

  1. Suppose that the social planner has determined precisely the additional social cost of the fertilizer runoff. The Marginal external cost is the additional external cost as a result of one more unit of output. In this case, MEC= 6.4*Q. Complete the table including Marginal External Cost (MEC) and Marginal Social Cost (MSC).
  2. In excel, graph demand, MC, and MSC all on one graph with Q always on the horizontal axis. (Graph 5 points)

  1. Determine the socially efficient equilibrium price and quantity.

P*=1420 Q*=50 (3points)

  1. Compare this to the inefficient market equilibrium that does not account for the social costs. How dose price and quantity change?

Inefficient market equilibrium price is lower and quantity is higher than that of socially efficient equilibrium. (3 points)

  1. Suppose that the government impose a 320$/ton tax on firms. Complete the remaining column of MC+tax. Graph MC+tax in the same graph of part (d).
  2. With the tax, what are the new equilibrium price and quantity? What is the government revenue?

P*=1420 Q*=50 Tax Rev=16000 (4 points)

  1. Have we achieved the social efficient solution from tax? Explain

Yes. Because marginal benefit= marginal social cost (2points)

2.The following are the (hypothetical) supply and demand schedules for ag business graduates:(30 points in total)

Supply:Wage = 10,000 + 0.6 Graduate

Demand:Wage = 90,000  1.4 Graduate

(Note: "Wage" is the price of labor in $/year, and "Graduate" is the number of ag business graduates.)

a. Use Excel to plot the above supply and demand schedules. In the graph, show:

i. The quantity of ag business graduates hired in equilibrium.(2 pts)

ii. The equilibrium wage paid to ag business graduates.(2 pts)

iii. The total income received by all ag business graduates in equilibrium. (2 pts)

iv. The economic rent received by ag business graduates in equilibrium.(2 pts)

v. The opportunity cost of ag business graduates in equilibrium.(2 pts)

Note: "Total Income" is equal to the "Rent" plus "Opportunity Cost" areas.


b.Calculate analytically (i.e., algebraically) the following amounts:(2 pts)

  1. The quantity of ag business graduates hired in equilibrium.

The equilibrium quantity is 40,000 ag business graduates hired. Equilibrium wages and quantities are those where supply intersects with demand:

90,000  1.4 Graduate = 10,000 + 0.6 Graduate

So:90,000  10,000 = 1.4 Graduate + 0.6 Graduate

2 Graduate = 80,000

Graduate = 40,000

  1. The equilibrium wage paid to ag business graduates.(2 pts)

The equilibrium wage is $34,000/year. Plugging in the equilibrium number of graduates obtained in point (1.b.i) (i.e., 40,000) in either the supply or the demand equation yields the equilibrium wage:

Wage = 90,000  1.4 Graduate = 90,000 - (1.4) (40,000) = $34,000/year.

  1. The total income received by all ag business graduates in equilibrium.(2 pts)

Total income is equal to the rectangle shown in the graph, which is equal to wage times quantity:

Income = ($34,000/year per graduate) (40,000 graduates) = $1.36 billion per year

  1. The economic rent received by ag business graduates in equilibrium.(2 pts)

Economic rent is the triangle shown in the graph (see point (1.a.iv)). The area of this rectangle is:

Economic rent = = $480 million per year

  1. The opportunity cost of ag business graduates in equilibrium.(2 pts)

Transfer earnings can be calculated either as the area of the trapezoid in the figure or, more easily, from the fact that:

Income = Economic Rent + Opportunity Cost

1,360 million = 480 million + Opportunity Cost

So:Opportunity Cost = $880 million per year

  1. Suppose now that the demand curve stays unchanged at

Demand:Wage = 90,000  1.4 Graduate,

and that the equilibrium quantity and the equilibrium wage also stay unchanged at the levels found in point (1.b.i) and (1.b.ii), respectively. However, assume that the supply curve of ag business graduates becomes more elastic. Make a new graph of demand and supply to help you answer to the following three questions.(Graph 4 pts)

i. Will the total income received by all ag business graduates increase, decrease, or remain unchanged?(2 pts)

Total income is calculated as equilibrium quantity times equilibrium wage. Both equilibrium wages and equilibrium quantities stay unchanged; hence, total income must stay unchanged as well.

ii. Will the economic rent received by ag business graduates increase, decrease, or remain unchanged?(2 pts)

As shown in the figure below, the economic rent will decrease.

iii. Will the opportunity cost of ag business graduates increase, decrease, or stay unchanged?(2 pts)

As shown in the figure below, the opportunity cost will increase. This must be the case, because total income stayed unchanged and the economic rent decreased.


3.Consider a 2,000-acre parcel of Iowa farmland, with typical yields of 160 bu/acre of corn and 50 bu/acre of soybeans. Assume also that: (30 points in total)

  • The production plan is a 45:55 corn:soybeans rotation (i.e., assume that 900 acres of corn and 1,100 acres of soybeans are planted each year), regardless of the corn and soybean prices.
  • The price of corn is $4.50/bu and the price of soybeans is $9.0/bu.
  • The non-land cost of production (which includes all costs except for the cost of renting the farmland) is$300/ac for corn and $180/ac for soybeans.
  • The annual interest rate is 5.50%.
  • There is no inflation.

a. Calculate the maximum annual rent per acre one would be willing to pay for this parcel of farmland. (5 points)

One would be willing to rent this parcel of farmland as long as it provides positive profits. Hence, the maximum annual rent that one would pay is the rent that would make profits equal to zero:

Profits = (900 acres) ($4.50/bu 160bu/ac  $300/ac)

+ (1,100 acres) ($9.0/bu  50 bu/ac  $180/ac)  Rent = 0

Rent = $378,000 + $297,000 = $675,000.

So, the maximum rent one would be willing to pay for this parcel is $337.50/ac.

b. Assuming that there exists a competitive market for farmland, and that the rent will remain constant in the future, calculate the price per acre for this parcel of farmland. (Hint: Remember that the present value (PV) of an amount (rent) received into the infinite future is given by:

PV = = ,

where r is the interest rate.) (5 points)

Using the PV formula, PV = 337.5/0.055 = 6136.36. Hence, the price for this parcel of farmland is $6136.36/ac.

c. Using the price you calculated in point (4.b), calculate the annual "yield" (i.e., the annual net rate of return in percent) from this parcel of farmland.(5 points)

Using the PV formula again, 6136.36.= 337.5/rr = 337.5/6136.36 = 5.5%. Hence, the annual "yield" from this parcel of farmland is 5.50%.

d. If the interest rate falls to 4%, would potential investors be interested in buying this piece of farmland at the price you calculated in point (3.b)? Explain your answer.(5 points)

If the interest rate falls to 4%, potential investors would be interested in buying this piece of farmland at a price of $6136.36/ac. This is true because, as shown in point (4.c), this parcel yields a net rate of return of 5.50% at a price of $6136.36/ac, which is greater than the 4% that investors can obtain elsewhere. Hence, investors will be interested in buying this parcel as long as it yields more than 4%. Alternatively, with an interest rate of 4% investors will be interested in buying this parcel, provided its price does not exceed $8,437.5/ac, because PV = 337.5/0.04 =8437.5.

e. Calculate the price per acre for this parcel of farmland if the interest rate increased to 8%.

Using the PV formula, PV = 337.5/0.08 = 4218.75. Hence, the price for this parcel of farmland would fall to $4218.75/ac if the interest rate increased to 8%. (5 points)

  1. Assume that a new economic study indicates that corn price will increase next year to $5.50/ac from $4.50/ac this year, and will stay at $5.50/ac forever because of a surge in corn demand from Asia. Calculate the impact of this increase in corn demand on the per acre price of this parcel of farmland, assuming an interest rate of 5.50%. How does this price compare with the price you calculated in point (4.b)?(5 points)

(Hint: PV = = + = + = + )

With the higher corn price, the maximum rent would be given by:

Profits = (900 acres) ($5.50/bu  160 bu/ac  $300/ac)

+ (1,100 acres) ($9.0/bu  50 bu/ac  $180/ac)  Rent = 0

Rent = $522,000 + $297,000 = $819,000.

So, the maximum per-acre rent for this parcel would be $409.50/ac. Plugging the corresponding values into the PV formula above, we get:

PV = + =7371.2

That is, the increase in corn price would cause the price of this parcel of farmland to go up from $6136.36/ac to $7371.22/ac.

4. (a) Name and describe the two characteristics of a public good. (5 points)

Nonexludable and Nonrival

(b) Name at least three examples of public good in society.(5 points)

…….