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1. An initial investment is invested at an annual rate of 1%. What was the initial value if after 5 years the value reached f2000, and the interest is compounded yearly? (round up the answers to 2 decimals)
2. If the average revenue is given by find the corresponding demand function Q(P) and estimate total and marginal revenue at Q=10
3. The cost of making Q kilograms of candy-floss is C(Q) = 5 + 20Q + 0.1Q2 dollars (round up to 3 decimals)
(a) If Q = 10, what is the marginal cost of candy-floss? State the units
of measurement
(b) If Q = 10, what is the elasticity of cost with respect to quantity
produced? State the units of measurement.
4. A firm’s production function is given by Y = F (K, L) = 4K0.4 L0.6 , where K is the amount of capital and L the amount of labour employed
(a) Evaluate
(b) What is the economic interpretation of ?
(c) Find the elasticity of output with respect to labour
5. Consider the three-commodity market model defined by:
(a) Find the equilibrium price and quantity in each market using the
inverse matrix method,
(b) How do the equilibrium prices change if the government levies a per-
unit tax of 2 pounds on suppliers in each commodity market.
6. A building supplier is allowed to charge different prices to its trade and individual customers. The corresponding demand equations are given by:
respectively. The total cost function is TC = 100 + 10Q where Q = Q1 + Q2.
(a) Find the prices that the firm should charge its trade and individual
customers to maximise total profit;
(b) Calculate the elasticities at these prices and verify that the firm
charges the higher price in the market where the magnitude of the elasticity of demand is lower;
(c) What happens to the equilibrium prices and profits if the supplier is no longer allowed to charge different prices to its trade and individual customers.
7. Jean works at a bakery. Her hourly wage is 12 pounds an hour and she works 35 hours per week. She spends half of her income on housing and the rest to consume goods x1 and x2 . The unit price of x1 and x2 are 4 and 2 pounds, respectively.
Her utility function is given by:
(a) Write down Jean’s weekly budget constraint and briefly describe her
maximization problem;
(b) Find the utility-maximising values of x1 and x2 through the method
of substitution?
(c) Set up the Lagrangian and show that we find the same values for x1 and x2 , as derived under (ii).
2021-12-26