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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)
Given that the two factor of production are employed in a fixed proportion in the production process, what will be the shape of the corresponding isoquants and the value of the MRTS as more and more units of one factor of production is employed keeping constant the other factor of production?
The Long-run production function is given by; Y = 180 L1.2 K1.8 Where, Y = Output (mt/day), L = Labour (hours/mt) K = Capita (Rs/mt) a) Calculate Marginal Product of Labour (MPL) and Marginal Product of Capital (MPK), if L=12 and K=20 b) Derive the equation for Isoquent and graphically show it by assuming L= 10, 15, 20 25 and 30. c) Determine factor intensity and returns to scale of this production function. d) Prove that the elasticity of labour is 1.2 and elasticity of capital is 1.8
MRS of X for Y refers to the amount of Y the consumer is willing to give up in order to gain one additional unit of X (and still remain in the same indifference curve!) Exercise 1 Draw the indifference curve using the data in the table at the left. Calculate and check that MRS mentioned in the table are correct. Is the MRSxy a decreasing function in X?
Calculate consumer surplus for the demand curve P=1-Q and the supply curve P=1+Q
A short run production function Q=L^3-2L^2-4L+40. Determine the amount of laborers used to maximize production.
Suppose consumers face the utility function: U (Xi, Yt) = XiYt; for i = 1, 2, ... ... ... ..., M Firms face the cost function: Cj(qj) = q2j + F (a) Solve for equilibrium in perfect competition. (b) Show the effect of change in income on equilibrium quantity.
Given MUx = X, MUY = 4Y, Price of X is 3 Birr per unit and price of Y is also 3 Birr per unit. If the income of the consumer is 1200 Birr, find the amounts of X and Y that the consumer chooses to consume so as to maximize his utility.