Q1: the Market for Hog Hats Is Competitive and Demand Is Given by P=75-2Q While Supply

ECON 303

Fall 2003

Exam 1

Dr. Cary Deck

This exam consists of 4 written problems worth 25 points each. Your exam should contain 5 pages. Please write your name on the top of each page. Answer each question as best you can. Where appropriate you must show work in order to receive full credit. The exam is closed book. If you have any questions please raise your hand and someone will come to you. There is no talking allowed during the exam. The use of electronic devices other than approved calculators is prohibited. You have one hour and twenty minutes to complete this exam. Exams will not be accepted after the end of the exam has been announced.

Name:___________

Score:____________

Q1: The market for hog hats is competitive and demand is given by P=75-2Q while supply is given by P=15+Q. What price and quantity will trade in the market? (4 points)

To find Qe set prices equal: 75-2Q=15+Q or 3Q=60. Therefore Qe=20 and Pe=15+Qe=35.

Define consumer surplus and producer surplus. What are consumer surplus and producer surplus in this market? (6 points)

Consumer surplus is the benefit buyers receive from trading. It is the area below demand and above price for units that trade. Producer surplus is the benefit sellers receive from trading. It is the area below price and above supply for units that trade. In this market CS=.5*(75-35)*20=400 and PS=.5*(35-15)*20=200.

For each of the following explain what would happen to 1) the market price of hog hats, 2) the quantity of hog hats traded, 3) consumer surplus or producer surplus and why. (5 points each) [You should consider each change separately. You will not be able to determine the impact of the change on both consumer surplus and producer surplus.]

A technological advance allows hog hats to be produced using a cheaper plastic.

This causes supply to shift right. This will lead to a lower price and a larger quantity. CS will increase.

The price of cotton which is used to produce hog t-shirts increases and the cross price elasticity of hog hats and hog t-shirts equals -0.75.

As the price of cotton increases the supply curve for t-shirts will shift left, raising the price in this market. Since t-shirts and hats are compliments, this will cause demand for hats to shift left. Hence the price of hats and the quantity of hats will fall. PS will decrease.

The Waltons decide to give every student at the UA $1000 and hog hats are normal goods.

This will cause demand to shift right so the price and quantity of hats will increase and PS will increase.

Q2: Homer Simpson discovered a new agriculture crop, tomacco, that is a cross between tomatoes and tobacco. Demand for this crop is given by P=400-3Q and supply is given by P=Q. Calculate the elasticity of demand at equilibrium and at the choke price. (6 points)

Ed= dq/dp*P/Q. Since P=400-3Q we have Q=400/3-P/3. Hence dq/dp is -1/3. The equilibrium price and quantity are found by solving 400-3Q=Q or Q=100 and P=100. At equilibrium Ed=(-1/3)*100/100=-1/3. The choke price is where Q=0 on demand. The choke price is 400-3(0)=400. At the choke price Ed =(-1/3)*400/0 = -infinity.

As it turns out, tomacco is just as harmful and addictive as tobacco. In order to reduce the number of tomacco users, a tax of $20 per unit is being proposed. By how much would this tax reduce the quantity of tomacco consumed? (4 points) How much tax revenue would the government collect and what would be the dead weight loss of this tax? (4 points each) [You must sketch a figure to receive full credit.]

Supply with the tax is P=Q+20. So the new price and quantity in the market will be where 400-3Q=Q+20 or Q=95 and Pc=115. Since sellers have to pay the tax the only take home a price of 115-tax = 95. The reduction in consumption is 100 (the old Qe) – 95 (the new quantity)=5. DWL=.5*tax* quantity reduction =.5*20*5=$50. Tax revenue is tax * new quantity=20*95=$1900.

How much of the tax is paid by consumers and how much is paid by sellers? (4 points) Explain, based on your calculations, which side of the market is more inelastic. (3 points)

CTI=(new price-old price)* new quantity=(115-100)*95=1425

PTI=(old price- seller’s new take home price)* new quantity=(100-95)*95=475.

Since consumers pay more of the tax, demand is more inelastic.

Q3: Using partial derivates, calculate the slope of the following curves. (5 points each)

f(x,y)=x2y +2x+y at the point (2,2)

df/dx=2xy+2 and df/dy=x2+1. So dy/dx=-(2xy+2)/( x2+1). At (2,2) this is -10/5=-2

f(x,y)=x0.2y0.8 at the point (1,32)

df/dx= .2x-0.8y0.8 and df/dy= .8x0.2y-0.2 . So dy/dx=-(0.2y/0.8x)=-y/(4x). At (1,32) this is -32/4=-8.

Find the equation for the line passing through the points (6,2) and (0,5). (4 points)

[Your answer should be in slope y-intercept form.]

The slope is (5-2)/(0-6)=-1/2. We know (0,5) is the y-intercept. The equation is
y=-(1/2)x+5.

What are the x & y intercepts of the line 20=4x+10y? (3 points)
What is the slope of this line? (2 points)

The x-int is where y=0 so it is found by 20=4x+10(0) or 20=4x or x=5.

The y-int is where x=0 so it is found by 20=4(0)+10y or 20=10y or y=2.

We can rewrite equation as -10y=4x-20 or y= -(4/10)x+2. So the slope is -4/10 or -2/5. Alternatively you could find the slope between the two points: (2-0)/(0-5)= -2/5.

Sketch a graph of 10=x+y and xy=25. (4 points)
[You should plot both curves on one graph.]

Find all solution(s) to the following equation: q2-3q-28=0. (2 points)

Using the quadratic formula we have [–(-3)+(-32-4(1)(-28)).5]/[2(1)] = [3+(9+112).5]/2 = (3+11)/2. So we have q=7 and q= -4.

Q4: The domestic market for steel is characterized by D: P=150-Q and S: P=Q-10. The world price of steel is 25. With an open market and no regulation how many units would domestic suppliers sell, what price would consumers pay and what is producer surplus? (6 points)

With no regulation the price will be 25. At this price domestic sellers would produce 25=Q-10 or Q=35 units. PS=10*25+.5*(35-10)*25=562.5. Note that the y-intercept of S is negative so we have to divide the PS area into a rectangle and a triangle.

For political reasons the president decides to protect the domestic steel industry. One possibility is to impose a quota on the number of units that can be imported. The president’s plan is to allow only 20 units to be imported. Sketch a diagram of the impact of this plan. (4 points). Under this plan how many units would domestic suppliers produce, what is their producer surplus, what price would consumers pay? (2 points each)

Since P=Q-10 or Q=P+10 with no quota, importing 20 units would cause the quantity to be Q=P+10 +20 or Q=P+30 or P=Q-30. The new equilibrium in the market with the quota would be found by Q-30=150-Q or Q=90 (20 of which are imports) so P=150-90=60. So with this policy consumers would pay 60 and domestic producers would make 70 units. PS=10*60+.5*60*(70-10)=2400.

A lobbyist for the steel industry proposes yet another policy. Specifically, the lobbyist wants the domestic market closed so that no steel can be imported and wants the government to place a production quota of 40 units on the market. How many units would domestic producers sell, what would be their producer surplus under this plan, and what price would consumers pay? (2 points each)

With a production quota of 40, producers would sell 40 units. The price for 40 units would be P=150-Q=110. Producers only had to receive a price of 30 to make 40 units (this is from plugging Q=40 into P=Q-10). PS=(110-30)*40+30*10+.5*30*(40-10)=3950.

What price floor would have the same effect as the lobbyist’s plan if the market for steel is closed to international trade? (3 points)

A price floor of 110, the price consumers pay under the production quota.