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Why Marginal Utility MUy of XY + 2X equals X
The following data refers to the demand for money (M) and the rate of interest (R)
in for eight different economics:
M (In billions) 56 50 46 30 20 35 37 61
R% 6.3 4.6 5.1 7.3 8.9 5.3 6.7 3.5
a. Assuming a relationship i M R U , obtain the OLS estimators of
and
b. Calculate the coefficient of determination for the data and interpret its value
c. Test the hypothesis that interest rate influences demand for money
d. Compute the standard error of the regression coefficients and conduct test of
significance at the 5% level of significance.
e. If in a 9th economy the rate of interest is R=8.1, predict the demand for money(M)
in this economy.
Suppose that a researcher estimates a consumption function and obtains the
following results:
C=15+0.81Yd n=19 R2=0.99
(3.1) (18.7)
where C=Consumption, Yd=disposable income, and numbers in the parenthesis are the
‘t-ratios’
a. Test the significant of Yd statistically using t-ratios
b. Determine the estimated standard deviations of the parameter estimates
You are selling a product in an oligopoly market. What factors would motivate you to collude with other firms in the market?
(25 marks)
A perfectly competitive firm Cat Paradise sells clothing for cats. A cat-suit sells for $72 each. The fixed costs for production are $100. The total variable costs are $64 for one suit, $84 for two suits, $114 for three suits, $184 for four suits, and $270 for five suits.
a) In a table, calculate TR, MR, TC and MC for each output level (one to five suits).
(10 marks)
b) What is the profit maximizing quantity?
(5 marks)
c) If the advent of new and better technology in a perfectly competitive market leads to a large reduction in costs of production, how will this affect the market?
(10 marks)
A good is represented by a market demand curve Q = 100 – P. In this market, there are an unlimited number of potential firms whose cost curve is given as TC = Q + Q2.
a) What is the long run equilibrium price, assuming free entry of firms?
(8 marks)
b) How many firms will there be?
a) Despite being a small local sundry shop, I can always beat the price that Tesco charges for the same product. Tesco must pay rent on its store while I own my own shop and have no rent to pay. Discuss.
(10 marks)
b) Evaluate and explain these two statements.
1. An increase in fixed cost increases the minimum-cost output.
2. An increase in fixed cost increases marginal cost.
(10 marks)
Suppose that your company is offered a contract to produce 1,000 units of a good X per day. Your company uses labor and capital to produce good X. The quantity of labor used, L, is expressed by hours of work, and the wage rate is $10 per hour. The quantity of capital utilized, K, is expressed in machine-hours, and the rental rate per machine hour is $40.
Thus total cost of production is TC = 10L + 40K. The production function is given by Q = 20L 0.5 K 0.5. In the contract, your company is required to produce 1,000 of good X.
a) Using the Lagrange function, determine the amount of labor and capital to use to minimize the cost of producing 1,000 units of good X.
(14 marks)
b) Interpret lambda and what it means to your company.
(6 marks)
