the Short run Cobb Douglas cost curve is given by
where a>0 and B>0 and F are constants
A. identify the meaning of F in economic terms
B. Let
, so that
.
write down the average cost
. Note that the Note that the average cost is the slope of the line
from (0, 0) to (q, C(q)) on the graph of C(q) versus q.
C. Find the minimum of AC.
D. At this minimum level, compare the marginal cost to the average cost. Based on this, sketch the graph of C(q) versus q (it’s just a cubic curve shifted up), and identify the point where the marginal cost (which is the slope of what?) is equal to the average cost (which is the slope of what, as noted above?)—i.e. the point you’re looking for is where the tangent line goes through what other point?

the Short run Cobb Douglas cost curve is given by where a>0 and B>0 and F...
The Cobb-Douglas production function is given as: Q = AK1-aLa Where 0<a<1, a = .8, K =4 is the amount of capital, and L=16 is the number of unit of labor, and A = 12 is the measure of TECHNOLOGY INDEX a) Find the real wage of labor (marginal product of labor), W/P, (b) Find rate of return of capital (marginal product of capital), and (c) Discuss the insights of your findings. (d) Why is there not a large amount...
a. Suppose that a firm has the Cobb-Douglas production function = 12K0.75 0.25. Because this function exhibits returns to scale, the long-run average cost curve is , whereas the long-run total cost curve is upward-sloping, with slope. b. Now suppose that the firm's production function is = KL. Because this function exhibits returns to scale, the long-run average cost curve is upward-sloping , whereas the long-run total cost curve is upward-sloping, with slope. a. Suppose that a firm has the...
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...
A firm has a Cobb-Douglas production function q = AKL, where K denotes capital, L is labor, and A, a, b, are constants. ginal returns to labor in the short run if its production function is 1. Sketch an isoquant line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 2. On a separate graph, draw an isocost line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 3. On...
5, (20 points) Consider the following cost function: c(q:F)-F +109 + 뚤, where F > 0 represents the fixed cost F = c(QF). (a) (5 points) Compute the marginal cost function, MC(q) (q; F) b) (5 points) Show that the marginal cost function MC() is increasing. (c) (10 points) Recall the average cost function, AC(q; F) - Find (F the value of q (given F) at which AC(q; F) MC(4)
EXERCISE 1 COST MINIMIZATION, PART I Consider a firm with a Cobb-Douglas production function defined by the equation Q = 32K0.5 0.25 where Q is output, K the capital input and I the labour input. The prices of both production factors are given to the firm: labour costs w = 32 per unit, capital r = 16 per unit. Imagine that the firm wants to produce 512 units of output at minimum cost. (a) Determine the (unique) stationary point, say...
Gainesville airline's production function is given by a Cobb-Douglas form: Y = AL"K,a.B>0 where: Y =number of passengers carried per year A coefficient L number of pilots (labor) K number of aircraft (capital) Suppose that the annual wage for each pilot is p, and the "price" of each aircraft (amortized annual cost) is p 1. Derive the output cost function for the Gainesville airline 2. Calculate the average and marginal cost functions, and discuss the condition when economies of scale...
4) Suppose each firm's long run average cost curve, for positive levels of output, is given by AC 0.10.05Q+5/Q. The marginal cost curve is given by MC 0.+0.1Q. (a) Find the minimum efficient scale for the above cost function (b) What is the firm's minimum average cost? (c) Suppose you have many identical firms in a long run competitive equilibrium. Demand is P 13.1-0.040. What is the market quantity? How many firms are there? (d) Suppose demand increases to P...
This graph shows a demand curve from point E to point S, an
average cost curve labeled AC, a marginal cost curve labeled MC,
and a marginal revenue curve labeled MR. Under average-cost
pricing, the equilibrium price and output in the market are _____,
respectively.
(A) B and R
(B) A and T
(C) C and Q
(D) D and P
(E) A and Q
Price - MC MR R T S Quantity
1. A. Graph the short-run supply curve for a perfectly competitive firm and explain where this short-run supply curve lies. Indicate the following curves on your graph: marginal cost curve, marginal revenue curve, average-total-cost curve, average-variable-cost curve, short-run supply curve. B Complete the chart for Elmer's Wheat farm. Quantity of Output Total Cost Average Total Cost Marginal Cost Price Total Revenue Marginal Revenue Profit/ Loss 0 $75 $ --- $ --- $ --- $0 $ --- - $75 1 220...