6. A firm's production function is given by q 20(EV2 +K2), where q is output and...
1. Suppose that a firm's production function of output Q is a function of only two inputs, labor (L) and capital (K) and can be written Q = 25LK. Letting the wage rate for labor be w and the rental rate of capital be r, the equation for the firm's demand for capital would be: wQ A) K = 25r B) K = C) K- 25r wQ rQ 25w 25w rQ 25wQ D) E) KE
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and both wage and interest rates are equal to one, so that war- a) Given that the wage increases to 4. determine the elasticity of demand for labour at the new wage. Indicate whether the wage bill will increase or decrease as wage increases to 6. b) Find the linear demand function for labour...
Afir's production engineers have estimated its production function as Q(KL) = 2K2/1/2 = 2-K L=2KL where ' and 'L' represent the amounts of capital and labour, respectively, used in production each period, and 'Q' represents the amount of output produced each period. The firm pays a wage, w, for each person-hour of labour of $16. The rental rate of a machine-hour of capital, wk, is $100. What will be the firm's minimum cost of producing 10 units of output? What...
Econ 10A: Problem Set 9 (1) A firm's production function is P(L, K) 2LV2K. Find the long-run profit-maximizing values of Land K when the wage for labor is w $10, the rental rate for capital is r $20, and the price of output is p $40.
Suppose the firm's production function is given by q= F(K, L)= K2L with MPL=K2, MPK=2KL The price per unit of capital is 10 and the price per unit of labor is 5. Find the cost minimizing quantity of labor to produce 500,000 units of output. Please round to the closest integer.
A firm's Cobb-Douglas production function for output x is f(l,k)= 25/5k5, where / (labour) and k (capital) 9. are variable inputs costing w (wage rate) and r (rental cost of capital) each per unit (a) Follow the two-step (indirect) method' and begin by setting up the firm's cost- minimisation problem and deriving the three first-order conditions (FOC8) (4 marks) 2(wr)2 x2 (where, to be clear, (c) The cost function derived from the FOC8 above is c(w,r,x) 3125 1 5 the...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
Suppose the firm's production function is Q = K1/3L2/3. a. If the rental rate of capital R = $30 and the wage rate W = $40, what is the cost-minimizing capital-to-labor ratio? b. If the rental rate of capital R is $35 and the wage rate W is $70, and assuming the same production function, how many units of labor and capital should the firm use to produce 12 units of output? c. What is the total cost of producing...
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if...
Suppose a firm's production function is given by the equation Q = 12L.5K.5 . This firm operates in the short run where capital (K) is fixed at a quantity of 16. If the price per unit of the good is $1.8 and labor costs $10 per unit. Then the profit maximizing amount of labor in the short run is ___?