Download EC109 – Microeconomics 1

EC109 – Microeconomics 1
Q1: Consider the following demand and supply functions.
Qd = 950 – 10p
Qs = - 400 + 20p
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What is the market equilibrium price?
At the market equilibrium price, what is the residual demand curve for a given firm?
At the market price of £39, what is the residual demand curve for a given firm?
What is the slope of the residual demand curve?
Q2: Consider 2 firms, A and B in the same market that are both price takers. Output is sold at £20
per unit and each firm faces a fixed cost of £35. The Total Variable Cost functions for each firm are
as follows:
TVCA = 0.5XA3 – 8XA2 + 48XA
TVCB = 0.5XB3 – 10XB2 + 75XB
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Find an equation for each firm’s marginal cost curve. Confirm that these curves are Ushaped.
What is the profit maximising output for each firm?
In the previous question why were there 2 answers for each firm? What does the other
answer that is not the profit maximising output represent?
What are the actual profits made by each firm?
Which firm should shut down? Prove your answer.
Q3: A consumer purchases 2 goods, food x and clothing y. He has the utility function
U (x, y) = xy. His income is £72 and the price of clothing is £1 per unit. Suppose the price of food
falls from £9 to £4 per unit.
(a)
(b)
(c)
(d)
(e)
What is the consumer's original consumption bundle?
What is the consumer's new consumption bundle (after the price fall)?
Calculate the compensating variation.
Calculate the equivalent variation.
What can we say about your answers to parts c and d?
Q4: Consider two uncertain outcomes having a 50% probability of occurring, with outcomes
denoted W1 and W2. Assume a household has the expected utility function:
U (W) = 10W – W2.
(a) Write down the inequality that shows when the household will be risk averse.
(b) Evaluate the inequality, if W1 = 2 and W2 = 4.
(c) Draw the expected utility function and identify both levels of utility and the expected
wealth.
(d) How do we know that this household experiences diminishing marginal utility of wealth?
Q5: Consider a perfectly competitive firm facing an output price of Pe = £12 with the following
short-run total cost function: STC = q2 + 10q + 1.
(a) Write out the firm’s profit maximization problem and calculate how many units (q) the
firm will sell at the market price of £12. What will be the firm’s profit?
(b) If the market price now falls to £11, what happens to the firm’s profits? Based on your
answer, should the firm remain in business?
Q6: Assume a firm faces the following cost curve and demand curves for markets X and Y.
TC = 20 + 4Q + Q2
Px = 100 – 2Qx
Py = 76 – Qy
(a) When a firm separates the market into 2 distinct segments, we refer to it as third degree
price discrimination. What conditions are necessary to allow this type of price
discrimination to occur?
(b) Find the total profit function across the two markets combined.
(c) What are the profit maximising prices and outputs in markets X and Y when a firm
price discriminates?
(d) Calculate the firm's total profit if it engages in price discrimination.
(e) Does the firm benefit from engaging in this type of price discrimination?
Q7: If Amanda spent her entire allowance, she could afford 8 chocolate bars and 8 comic books per
week. She could also afford 10 chocolate bars and 4 comic books per week. The price of chocolate
bars is 50 pence.
(a) Graph her budget constraint and find her weekly allowance.
(b) If it is the case that when Amanda buys more than 10 chocolate bars, the price of additional
chocolate bars (beyond 10) drops to 25 pence each, graph her new budget constraint.
Q8: At your high-school’s fund raising picnic, you pay for soft drinks with tickets purchased in
advance – one ticket per bottle of soft drink. Tickets are available in sets of three types:
Small: £3 for 3 tickets
Medium: £4 for 5 tickets
Large: £5 for 8 tickets.
The total amount you have to spend is £12. If fractional sets of tickets cannot be bought
(and no resale of tickets is possible), graph your budget constraint for soft drinks and the
composite good.
Q9: Shirley Sixpack and Lorraine Quiche are friends. Shirley thinks a 16-ounce can of beer is just as
good as two 8-ounce cans. Lorraine only drinks 8 ounces at a time and hates stale beer, so she
thinks a 16-ounce can is no better or worse than an 8-ounce can.
(a) Write a utility function that represents Shirley's preferences between commodity bundles
comprised of 8-ounce cans and 16-ounce cans of beer. Let X stand for the number of 8-ounce
cans and Y stand for the number of 16-ounce cans.
(b) Write down a utility function to represent Lorraine’s preferences.
(c) Would the function utility U(X, Y ) = 100X+200Y represent Shirley's preferences? How about
U(X,Y) = X + 3Y?
Q10: How do the predictions of the monopoly, Cournot, Bertrand and Stackelberg models differ
concerning the equilibrium quantity?