Microeconomics Answers

This question has two independent parts:
(a) Consider the following game. There are ten dollars to divide.
Two players are each required to simultaneously name an integer
between 0 and 10. The player who names the higher number gets
to keep the money. If they name the same number, each player
receives nothing, i.e., 0
i. Find the best response function for each player.
ii. Are there strategies that are strictly dominated? Demonstrate
your reasoning. What are the resulting strategies after iter-
ated elimination of strictly dominated strategies?

Consider the following game of duopoly. Two rms produce the same
product at zero costs. Each of them simultaneously determines their
quantities. The demand function for the commodity is P(q1, q2) =
100 - q1 - q2, where qi, (i = 1, 2) denotes the quantity rm i produces.
Firm i's prots are therefore πi(q1, q2) = P(q1, q2)qi. Suppose that
each firm is allowed to choose from three quantities 50, 30, or 0.
(a) Represent the game in normal form/ matrix form.
(b) Are there any strictly dominated strategies for each player? Why,
or why not ?
(c) Find all the Nash Equilibria of the game

Firm produce output according to C.D technology Y=F(K,L)=AK^α L^(1-α). Derive short run profit maximising input demand, output supply and profit functions with this technology, ignoring firm's shutdown condition.

TRUE or FALSE. (25 points) All credits are assigned to explanations.
You need to provide adequate explanations to obtain any credit.
(c) Tom's world also consists of Lasagna (l) and Chocolates (c). Tom
however, has the following preference over bundles of l and c: Tom
strictly prefers the bundle (L*; C*) = (5; 5) to any other bundle.
Based on this we can conclude that Tom's preference is strictly
monotonic.
(d) A consumer consumes apple pie and ice cream. She considers
them perfect complements to each other. Then, she must become
strictly worse o_ when the price of ice cream increases.

(e) In the _rst price sealed bid auction with perfect information, if
bidder i has valuation vi, then a bid bi < vi is weakly dominated
by the bid vi

TRUE or FALSE. (25 points) All credits are assigned to explanations.
You need to provide adequate explanations to obtain any credit.

(a) A consumer has strictly monotonic preferences that can be repre-
sented by a utility function. She chooses bundle A under certain
prices and income. Furthermore, bundle A is cheaper than bundle
B under those prices. If prices change and bundle B becomes more
expensive than bundle A, it is possible for the consumer to choose
bundle B instead.

(b) Jerry's world consists of two commodities Lasagna and Choco-
lates. Given any two bundles consisting of Lasagna and Choco-
lates, Jerry always prefers the bundle that has more lasagna. Only
in the case where two bundles have the same amount of lasagna,
Jerry prefers the bundle with more Chocolates. Then, Jerry's
preferences are complete.

Greg’s Hardware has determined the following demand and supply equations for nails
QD = 10,000-25P
QS = -5,000 + 50P
a. How many nails would be sold for $100?
b. At what price would nail sales be zero?
c. When P = $200, what is total revenue? What is marginal revenue?
d. What is the relationship between quantity supplied and quantity demanded at a price of $300?

CARICOM Products Limited production function is lnQ = 0.63 + 0.43lnK + 0.56lnL. Given that price of labour (L) is $20 and the price of capital (K) is $33

(i) What is the optimal mix?
(ii) What is the firm’s output elasticity and returns to scale? Explain.

Question 3 (20 marks)
A firm has the following short-run production function:
Q = 50L+6L 2 −0.5L 3
where Q = Quantity of output per week
L = Labor (number of workers)
a. When does the law of diminishing returns take effect?
b. Calculate the range of values for labor over which Stages I, II, and III occur.
c. Assume each worker is paid $10 per hour and works a 40-hour week. How many workers should the firm hire if the price of the output is $10? Suppose the price of the output falls to $7.50. What do you think would be the short-run impact on the firm’s production? The long-run impact?

Fence Right is a firm that supplies and installs fence. Its output follows the production function
Q = 20L – 0.5L2; where L denotes labour hours and Q the length of the fence in feet. The firm
hires labour at a wage of $25 per hour.
Hint: MRPL = MRC
a) DD has received an offer to install 200 feet of fence for a price of $480. Should DD accept
the offer?
b) What offer would be profitable if the company desires a price of $5 per foot of fence installed
(show all workings)?

Low-skilled workers operate in a competitive market. The labor supply is QS = 10W (where W is the price
of labor measured by the hourly wage) and the demand for labor is QD = 240 – 20W. Q measures the
quantity of labor employed (in thousands of hours).
a. Find the equilibrium wage (W) and quantity (Q) of low-skilled labor workers in equilibrium.
b. If the government passes a minimum wage of $10 per hour, what will be the new quantity of labor (Q)
demanded? Comparing labour demand and supply at the minimum price, will there be a shortage or
surplus of labor? How large?
c. Calculate the deadweight loss of this price floor.
d. By comparing the producers’ surplus before and after the minimum wage is introduced, how much
better off are low-skilled workers in this case? How much worse off are employers?