Write a 2 to 3 page paper (including screen captures) on Public Key Authentication. In what ways are public keys effective and in what ways can they be compromised? Test….

## Suppose a firm faces a ‘Cobb-Douglas’ production function: Q = 0.5K0.5 L 0.5 where Q is output, and K and L are the amounts of capital and labour used in the production process. The marginal productivities associated with this production function are MPL = 0.25L -0.5K 0.5 and MPK = 0.25L 0.5K -0.5 . Labour costs (W) are €10 per hour and capital costs (R) are also €10 per hour. a. If the firm is operating efficiently, what is the cost of producing 100 units of output? How many units of labour and of capital will be employed? b. If, in the short run, the amount of input K is fixed at K = 75, how much labour would be needed to produce an output of 100? c. When K is fixed at 75, and 100 units of output are produced, by how much do short-run costs exceeds costs in the long run? d. When K is free to vary, what inputs will the firm use if the rental rate doubles to €20, W is unchanged and if the firm still wishes to produce 100 units of output?

**Question 1**

The demand for ice cream is given by Qd = 20 –P where quantity is measured in gallons. Ice cream can be supplied for: Qs = P – 10.

a. What is the equilibrium price and quantity in this market?

b. Suppose the government introduces a €1 tax on ice cream, collected from the buyer. Write down the new post-tax demand curve.

c. After the tax is introduced, how many gallons are sold in equilibrium? What price is paid by buyers? What price is received by sellers?

d. How much of the impact of the tax falls on buyers and how much on sellers?

e. How much tax revenue is raised for the government?

f. Suppose the government decides to switch the tax to one collected from sellers. What is the new post-tax supply curve?

g. With the tax collected from sellers, what is the equilibrium quantity, the equilibrium price paid by buyers and that received by sellers?

h. Comment very briefly on the outcomes under c) and g)

**QUESTION 2** Consider a market with inverse demand function P = 9 – 2Q and a firm with MC = 0.5.

a. Find the equilibrium price and quantity in a competitive market where the single firm acts as a price taker.

b. Calculate the consumer surplus and the producer surplus under competition.

c. Determine the equilibrium price and quantity when the firm acts as a monopoly and charges a single price.

d. Calculate the consumer surplus and producer surplus under the monopoly solution.

**QUESTION 3**

The sole promoter of a sports tournament estimates that the demand for tickets by adults is Qad = 5000 – 10P and by students is Qsd = 10000 – 100P. Average and marginal cost are estimated to be constant at €10. The promoter wishes to segment the market and to charge adults and students different prices. EF210 – Intermediate Microeconomics Semester 1 Examinations 2015/2016 Page 3 of 3

a. Determine the amount sold in each segment of the market.

b. What price is charged in each sub-market? Who pays more?

c. If the firm did not price discriminate, what price would it charge?

d. What profit is earned under price discrimination and under a single price?

**Question 4**

Suppose a firm faces a ‘Cobb-Douglas’ production function: Q = 0.5K0.5 L 0.5 where Q is output, and K and L are the amounts of capital and labour used in the production process. The marginal productivities associated with this production function are MPL = 0.25L -0.5K 0.5 and MPK = 0.25L 0.5K -0.5 . Labour costs (W) are €10 per hour and capital costs (R) are also €10 per hour.

a. If the firm is operating efficiently, what is the cost of producing 100 units of output? How many units of labour and of capital will be employed?

b. If, in the short run, the amount of input K is fixed at K = 75, how much labour would be needed to produce an output of 100?

c. When K is fixed at 75, and 100 units of output are produced, by how much do short-run costs exceeds costs in the long run?

d. When K is free to vary, what inputs will the firm use if the rental rate doubles to €20, W is unchanged and if the firm still wishes to produce 100 units of output?

**Question 5**

Suppose the market demand for roses is Qd = 100 – Q which is supplied by two firms A and B. Each firm has constant average and marginal cost of €5.

a. If firms collude and behave as a monopoly, how many roses will each produce, at what price, and how much profit will each firm make?

b. Suppose, instead, the firms behave like (Cournot) oligopolists, taking each other’s production as given, and calculating their own profit-maximising production; what output will each produce, and what profit will each earn?

c. Finally, if the firms compete on price (Bertrand oligopoly), what will be the price of roses, and how many will be sold in total? Will the firms earn a profit?

d. Give brief reasons for the different outcomes.