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Production Analysis Q. I The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q =13 1PKG where O is number of trucks produced per week. & is number of labor hours per day, and & is the daily usage of capital investment. a. Does the equation exhibit increasing, constant, or decreasing returns to scale? Why? b. How many trucks will be produced per week with the following amounts of labor and capital? Labor Capital 100 50 120 50 150 75 200 100 300 150 c. If capital and labor both are increased by 10 percent. what will be the percentage increase in quantity produced? d. Assume only labor increases by 10 percent. What will be the percentage increase in production? What does this result imply about marginal product of labor? e. Assume only capital increases by 10 percent. What will be the percentage increase in production? f. How would your answers change if the production function were -1.3 [WA " instead? What are the implications of this production function? Show in graph. Q. 2 Show in a diagram what changes will occur as a result of the changes listed. a. The firm's budget increases. b. The price of Y decreases. c. The price of X decreases. d. Y becomes more expensive, and X becomes less expensive. e. Technology makes the Y input more productive. f. Technology increases the productivity of both inputs by the same proportion. Q.3 The owner of a car wash is trying to decide on the number of people to employ based on the following short-run production function: Q= 66 - 0.56- where Q is Number of car washes per hour, L is Number of workers a, Generate a schedule showing total product, average product, and marginal product. b. Suppose the price of a basic car wash in his area of business is $5. How many people should he hire if he pays each worker $6/hour? c. Suppose he considers hiring students on a part-time basis for S/hour. Do you think he should hire more workers at this lower rate? Explain, Q.4 In a wheat market: Qd = 3550 -266P and Q3 - 1800 + 240 P I, Find the equilibrium for this market both numerically and graphically. Il. Find the point price elasticity of demand and the point-price elasticity of supply at the equilibrium price. Are the producers going to gain in terms of their total revenue if there is an increase in price? Explain. Ill. Following a severe drought the regulators in this market wish to boost production in this market. They decide to implement a price floor by choosing a price higher the equilibrium market price. Explain the impact of such a policy on the quantity of wheat that will be bought and sold in the market and its impact on efficiency. Is this going to create a gap between demand and supply? Explain using an appropriate graph. IV. Do you think that the Indian Policy makers have ever used such a price-policy?Suppose you are estimating parameters of the following regression model: Where: I'm = average starting pay at graduation, in pounds. N'a = tuition fee in 2012, in pounds. X's = independent recruiter rating (maximum is 5.0). 1 = disturbance term. Using cross-section data on top 50 UK graduate business schools, you obtain the following results: Y, = 9941 + 0.25 X2 + 15125 X31 (6114) (0.121) (7349) R' = 0.87. RSS = 10310 The figures in parentheses are the estimated standard errors. RSS are residual sum of squares.) (i) Comment on the signs of the variables in the model. (2 Marks) (ii) Interpret and explain individual coefficients. (4 Marks] (iii) Suppose X's increases by 0.25; what is the expected impact of this change on Y? (2 Marks) (iv) Comment on the explanatory power of the regression. (2 Marks) (v) Using t-tests show whether individual coefficients are significantly different from zero at 5% level of significance. (4 Marks) (vi) Test whether the coefficient of X, is significantly different from 1 at 5% level of significance. (2 Marks) (vii) Carry out an appropriate test to check if coefficients are jointly significant. (5 Marks)a) the marginal product of the 6" unit of labor? b) at what level of labor APL and MPL equal? c) the total cost of producing 455 units of output 3. Assume a firm with a production function O=122"*