One.

Assume a monopolistically competitive car industry.

The demand facing any given producer is given by

Qi = S [(1/N) - (1/30,000)(Pi - PA)]

where Q is the firm's sales

S is the total sales of the industry (size of the market)

N is the number of firms in the industry

Pi is the price charged by the firm itself

PA is the average price charged by the firm 's competitors

The total cost function for producing cars is

C= 750,000,000 + 5000Q

Now, suppose that there are two countries: Home and Foreign. Home has annual sales of 900,000 cars and Foreign has annual sales of 1.6 million. The two countries have the same cost of production.

Derive the PP and CC relationships for Home and determine the equilibrium price and number of firms.(10)

Derive the PP and CC relationships for Foreign and determine the equilibrium price and number of firms.(10)

Now assume no transportation cost and that it is possible for Home and Foreign to trade cars with one another. Derive the PP and CC relationships for this integrated market and determine the equilibrium price and number of firms.(10)

Suppose that the two countries were to integrate their car market with a third country with an annual market for 3.75 million cars. Find the number of firms, the output per firm and the price per car in the new integrated market after trade.

Two.

1. Let the market demand curve be P=1000 - 10Q. Assume the market is controlled by a monopolist. Let fixed cost be $10,000 and Marginal Costs (MC)=20Q.

a) What is the profit maximizing output?

b) What is the monopolist's total revenue at the profit maximizing output?

c) How much profit is the monopolist earning?

d) Assume the government breaks up the monopolist in order to create perfectly competitive market of identical firms. Assume the MC curve is now the industry supply curve. By how much has consumer surplus increased from breaking up the monopolist?

e) What is the deadweight loss associated with the monopolist relative to the perfectly competitive market?

2. Suppose a firm's fixed costs are $50 and its marginal cost of producing q units is MC = 10 + 2q. The industry demand curve is given by P = 40 - QD (where quantity is given in thousands of units). If the firm operates in a perfectly competitive industry and the price of the good is $30, how many firms produce this good in the short run?

3.

Price: Quantity:

8300

7400

6 500

5 600

4 700

3 800

2 900

1 1000

The monopolist has fixed costs of $1,000 and has a constant marginal cost of $2 per unit. If the monopolist were able to perfectly price discriminate, how many units would it sell?

Show the work for each question.

C...

Work out the following.

Question 1: Louis the retired Canadian lives on a fixed budget and consumes only two goods: toques (T) and maple syrup (M). Suppose Louis' monthly budget is 100 and the price of the two goods are (PT, PM) = (4,2). (a) Make a properly labeled diagram illustrating Louis' budget constraint with T on the hori- zontal axis and M on the vertical axis. Indicate the area corresponding to the set of bundles (M, T) that Louis can afford (b) What is the maximum T that Louis can afford? What about the maximum M? (c) What is the slope of the budget line, and what is the economic interpretation of it? (d) Suppose the Canadian government decides to ration maple syrup, limiting each person to a maximum of 40 units of maple syrup per month. Draw a new diagram showing Louis' new budget constraint and indicate the area corresponding to the set of bundles that Louis can afford now. Question 2: Annie and Marty are both single parents with full-time jobs. Consequently, both value child care services (5) and children's clothing (C) but may have different preferences for the two goods. The government decides it wants to make life easier for single parents and is considering providing single parents with monthly child care vouchers or, simply, providing single parents with a cash payment every month. Suppose Annie and Marty's incomes are both 400, the price per unit of child care is 10 per unit and the price per unit of clothing is 20. (a) Draw Annie's budget constraint assuming the government decides to offer a $100 voucher for child care. (b) Draw Marty's budget constraint assuming the government decides to offer a $100 cash payment to single parents. (c) Draw an indifference curve representing Annie's preferences that is consistent with Annie strictly preferring the cash payment to the voucher. (d) Draw an indifference curve representing Marty's preferences that is consistent with Marty being indifferent between the cash payment and the voucher. Question 3: After winning the lottery, Australian Artie decides to retire, stay home, and watch sports on television all day. Artie likes both Rugby, R, and Aussie Rules Football, F and views them as imperfect substitutes. In particular, Artie's preferences can be represented by the follow- ing utility function: U = R04Foe. Since Artie is rich, the only cost of watching F is the opportunity cost of not watching R: one hour of R necessarily means one hour less of F. In other words, even though Artie is rich, there is still a price on his time. 1-2 of 2(a) What is Artie's marginal rate of substitution between R and F, MRSay? Interpret it. (b) What is the price ratio, PR/PF? Interpret it. (c) Suppose Artie chooses some bundle, (R, F). If this bundle maximizes Artie's utility, what relationship must hold between R and F? (d) Define ME. What is the interpretation of this? If Artie is maximizing his utility, what must FR MUs be equal to? (e) Suppose there are 24 hours in a day. What bundle (R, F) will Artie consume? [Now you should find actual numbers.] Question 4: Picky Pete drags Indifferent lan out for coffee at an upscale Italian cafe which sells only espresso (E) and biscotti (B). Picky Pete simply must have one biscotti for every espresso consumed, whereas Indifferent lan views espresso and biscotti as perfect substitutes. One of their utility functions is given by U = min [E, B] and the other's by U = E + B. (a) Given the description, which utility function corresponds to which person? (b) Suppose the prices of the goods are (PEPs) = (2,1) and Pete has allocated $12 for the outing while lan brought only $4. Solve for each person's utility-maximizing bundle of espresso and biscotti. (c) Draw a fully labeled diagram illustrating Pete's budget constraint, his optimal bundle, and an indifference curve representative of his utility at his optimal bundle. Indicate how much utility Pete obtains. (d) Do the same for Ian. Question 5: Energetic Erin consumes a worrisome amount of caffeinated beverages, particularly soda (S) and coffee (C). A utility function representing her preferences is given by U = 450503. Erin's Income is 120 and the prices of the two drinks are given by (ps. pc) = (4,2). (a) Solve for Erin's utility maximizing bundle of beverages and calculate how much utility she obtains from it. (b) Suppose Erin moves to Berkeley where there is a soda tax and, consequently, the price of soda is 6. Solve for Erin's new utility maximizing bundle of beverages and calculate how much utility she obtains now. What is the "total effect" of the price change on Erin's consumption of soda? (c) Draw a diagram showing Erin's budget constraint before and after the move, and repre- sentative indifference curves of her choices before and after the move. (d) The total effect you found in part "b" can be broken down into a "substitution effect" and an "income effect". What is the sign of: (i) the total effect, (ii) the substitution effect, and (iii) the income effect? Explain why for (ii) and (uil). 1-2 of 2