Homework Answers
Industry supply function of the summation of individual supply function
Q = qG + qM = (2P - 4) + (P - 3) = 2P - 4 + P - 3 = 3P - 7
Thus, industruy supply function is:
Q = 3P - 7
In the following diagram SS is the supply curve
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2. Scotch is made by two firms: Glenmorangie and Macallan. The individual supply functions for Glenmorangie...
2. Scotch is made by two firms: Glenmorangie and Macallan. The individual supply functions for Glenmorangie...
2. Scotch is made by two firms: Glenmorangie and Macallan. The individual supply functions for Glenmorangie and Macallan are as follows: Glemnorangie: q 2P- 4 Macallan Derive the industry supply function for Scotch (Q). Show the supply curve in a diagram with P on the vertical axis and Q on the horizontal axis.
3. There are two types of firms in an industry. Type 1 firms have the costs...
3. There are two types of firms in an industry. Type 1 firms have the costs TC(n) = 625+ 0.25qi and type 2 firms have costs TC(2) 50000.52 The fixed costs for both types of firms are NOT sunk. (a) Derive each firm's ATC(g), AVC() and MC() functions and plot the curves on separate diagrams (b) Derive each firm's supply function q(p) and show the corresponding curves in the diagrams (c Suppose that there are 10 firms of each type....
Assume that there are two firms in an industry, each producing with a constant marginal cost...
Assume that there are two firms in an industry, each producing with a constant marginal cost function of MC = 10. Assume that the demand function for the product is defined as follows: Q = 200 – 2P. a) Derive the best reaction functions for both firms. (5 marks) b) Determine the cournot equilibrium quantities and cournot equilibrium price. (5 marks)
Short Run Cost Curves: Consider two firms, producing different products, with the following production functions: q=5KL...
Short Run Cost Curves: Consider two firms, producing different products, with the following production functions: q=5KL (1) q=5(KL).5 (2) a. For a short-run situation in which K=100, and given wage = 3 and cost of capital = 1, derive expressions short run total cost for each production function. (Start by using the production function to develop an expression for L in terms of q, and then substitute that, and the given parameters, into the generic expression for Total Cost =...
5. Prove that when the production function is homogeneous of degree one, it may be as...
5. Prove that when the production function is homogeneous of degree one, it may be as f(x) 2MP(x)x where MPi(x) is the marginal product of input i. Hint use Euler's Theorem. 6. Derive the cost function for the linear technology y f(xix2)-axi+bx 7. Given the production function fxi)aIxa In(x), derive the firm's supply function assuming an interior solution, assuming that a>0 and a 0. 8. Consider a duopoly facing an industry demand function, p-a-bQ, where Q tg respective cost functions...
4. In the competit ve market for widgets there are 50 identical consumers and 200 iden tical firms. Each individual...
4. In the competit ve market for widgets there are 50 identical consumers and 200 iden tical firms. Each individual consumer has the following demand function for widgets P(P) 100 2P where qD is the quantity an individual consumes and P is the widget's price. Each firm has the following cost function: C() 100 2qq (a) (3 points) Find the market demand function for widgets QP(P). Find the industry supply function for widgets Qs(P), make sure to find each firm's...
200 5. Suppose you are given the following inverse demand function, p and the inverse supply...
200 5. Suppose you are given the following inverse demand function, p and the inverse supply Q+1 function, p=5+0.50. With p on the vertical axis and Q on the horizontal, draw these two functions. Also solve for the equilibrium Q* and equilibrium price p*. 6. Suppose the labour demand function is giverlas w = 18 - 1.6L and the labour supply function is given as w=6+0.4L. Determine the equilibrium wage and equilibrium number of workers algebraically. Draw the above labour...
Consider a market that faces the following market supply and demand functions Q^S = −2 +...
Consider a market that faces the following market supply and demand functions Q^S = −2 + 2p Q^D = 16 − p where identical firms face the total cost function of T C = 8 + 3q + 1/2q^2 a) What is the market price? b) Derive the average variable cost, average total cost, and marginal cost functions. c) In the short run, how much does each firm produce? d) In the short run, how much economic profit or loss...
2. (1.5 p) Consider perfectly competitive industry with identical firms. The long run average cots function...
2. (1.5 p) Consider perfectly competitive industry with identical firms. The long run average cots function of a typical firm is given by AC(q)- 24 - 49 + q. Market demand is given by c p)=100-2p. (a) Find the long run supply curve of the typical firm. (b) Find the number of firms in the industry in the long run equilibrium.
A market demand and supply functions are as follows: Qd = 500 - P/4, and Qs...
A market demand and supply functions are as follows: Qd = 500 - P/4, and Qs = P/2 - 100. For parts 2-5, use ONE graph. 1. Determine the equilibrium price and quantity. 2. Graph the inverse demand and supply curves with Q on the horizontal axis and P on the vertical axis. Clearly label all axes, curves, intercepts, and the equilibrium price and quantity values 3.Assume the government sets a rule that the selling price cannot go above $400....
2. Scotch is made by two firms: Glenmorangie and Macallan. The individual supply functions for Glenmorangie and Macallan are as follows: Glemnorangie: q 2P- 4 Macallan Derive the industry supply function for Scotch (Q). Show the supply curve in a diagram with P on the vertical axis and Q on the horizontal axis.
3. There are two types of firms in an industry. Type 1 firms have the costs TC(n) = 625+ 0.25qi and type 2 firms have costs TC(2) 50000.52 The fixed costs for both types of firms are NOT sunk. (a) Derive each firm's ATC(g), AVC() and MC() functions and plot the curves on separate diagrams (b) Derive each firm's supply function q(p) and show the corresponding curves in the diagrams (c Suppose that there are 10 firms of each type....
5. Prove that when the production function is homogeneous of degree one, it may be as f(x) 2MP(x)x where MPi(x) is the marginal product of input i. Hint use Euler's Theorem. 6. Derive the cost function for the linear technology y f(xix2)-axi+bx 7. Given the production function fxi)aIxa In(x), derive the firm's supply function assuming an interior solution, assuming that a>0 and a 0. 8. Consider a duopoly facing an industry demand function, p-a-bQ, where Q tg respective cost functions...
4. In the competit ve market for widgets there are 50 identical consumers and 200 iden tical firms. Each individual consumer has the following demand function for widgets P(P) 100 2P where qD is the quantity an individual consumes and P is the widget's price. Each firm has the following cost function: C() 100 2qq (a) (3 points) Find the market demand function for widgets QP(P). Find the industry supply function for widgets Qs(P), make sure to find each firm's...
200 5. Suppose you are given the following inverse demand function, p and the inverse supply Q+1 function, p=5+0.50. With p on the vertical axis and Q on the horizontal, draw these two functions. Also solve for the equilibrium Q* and equilibrium price p*. 6. Suppose the labour demand function is giverlas w = 18 - 1.6L and the labour supply function is given as w=6+0.4L. Determine the equilibrium wage and equilibrium number of workers algebraically. Draw the above labour...
2. (1.5 p) Consider perfectly competitive industry with identical firms. The long run average cots function of a typical firm is given by AC(q)- 24 - 49 + q. Market demand is given by c p)=100-2p. (a) Find the long run supply curve of the typical firm. (b) Find the number of firms in the industry in the long run equilibrium.
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