## In the game of matching pennies, each player has a penny and must secretly turn the penny to either heads or tails.

### economics

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Question 17

In the game of matching pennies, each player has a penny and must secretly turn the penny to either heads or tails. They then reveal their choices simultaneously. If the pennies match—both heads or both tails—player A keeps both pennies, so he wins one from player B. If the pennies do not match—one heads and one tails—B keeps both pennies, so she wins one from A. For instance, If the pennies match, A wins one penny and B loses one, so their payoffs are (1,-1). If they pennies don't match, A loses one and B wins one, so their payoffs are (-1,1).

i.                    Write down the payoff matrix for this game.

ii.                  What is meant by Nash equilibrium?

iii.                Does this game has a pure strategy Nash equilibrium/ equilibria? If not, then calculate the mixed strategy Nash equlibrium.

Question 24

The following five firms are in the sugar industry. Their sales are:

Firm A: sales= €35,000

Firm B: sales= €30,000

Firm C: sales= €25,000

Firm D: sales= €20,000

Firm E: sales= €15,000

There are also 3 other firms in this market, which have 5% of the market each.

a)      Calculate the market share of firms A to E.

b)      Calculate the 3-firm concentration ratio.

c)    Calculate the Herfindahl index (or H-index).

Question 31

i)                    Discuss all the make-or-buy fallacies.                                                                   [10 marks]

ii)                  What is the difference between complete and incomplete contracts? Explain all the factors that prevent complete contracting.                                                        [10 marks]

iii)                What are the advantages and disadvantages of using market firms?              [5 marks]

Question 37

Suppose a firm produces two products, X and Y. The production technology displays the following costs, where C(i,j) represents the cost of producing i units of X and j units of Y:

C(0,50) = 100  C(5,0) = 150

C(0,100) = 210 C(10,0) = 320

C(5,50) = 240  C(10,100) = 500

i.            Does this production technology display economies of scale? Why?

ii.            Does this production technology display economies of scope? Why?

iii.            How can one achieve economies of scale in purchasing?

iv.            Explain the relationship between economies of scale and specialization.

v.            What is a learning curve?

Question 42

The market for study desks is characterized by perfect competition. Firms and consumers are price takers and in the long run there is free entry and exit of firms in this industry. All firms are identical in terms of their technological capabilities. Thus the cost function as given below for a representative firm can be assumed to be the cost function faced by each firm in the industry. The total cost and marginal cost functions for the representative firm are given by the following equations:

Suppose that the market demand is given by:

i.            Find the marginal cost and average total cost for the firm.

ii.            What is the long-run equilibrium price and quantity in this market?

(Hint: in the long run MC= ATC)

When this industry is in long run, how many firms are there in this market? (Hint: firms are identically sized)