For the following total profit function of a firm, where X and Y are two goods sold by the firm:
Profit = 170X – 5X2 –XY -4Y2 +175Y -225
Do problem with a constraint of X + Y =30.
For the following total profit function of a firm, where X and Y are two goods...
у 1200- A firm has the marginal profit function below, where P(x) is the profit earned at x dollars per unit. dP 9000 - 3000x dx (x2 - 6x+ (+10) 2 600- 0- LY 6 8 -600- The graph of this function is shown to the right. Find the total-profit function given that P = $1500 at x = $3. -1200- How can the total-profit function be found? A. Substitute the given value of P into the marginal-profit function and...
Suppose the short run cost function for a competitive firm is C(Y)= 4Y2+ 200 where Y is the total output. Find the profit maximizing supply for the firm if the output price is $16 and the maximum profit. What is its short run decision: To produce or not to produce?
Problem 81 Find the point farthest from (1,3,-1) such that x2 + y2 + z2-11 and x-y+z < 3. What happens to the maximum distance if the 11 on the right side of the inequality is perturbed? 81. Suggestions (a) Take as objective the square of the distance from (x, y, z) to the point given (b) For the case of points inside the given sphere and with x-y+ z = 3, you might solve the Lagrange equations for x,...
7. (5 points) There are two firms X and Y. Firm X produces goods x and Firm Y produces goods y. The unit price of x is $1 and the unit price of y is $2. Labor is the only input of production. The wage rate for workers in Firm X is $20 while the wage rate for workers in Firm Y is $15. The production function of the paper mill is However, since the paper mill drains chemical waste...
Consider two freely available goods, X and Y. (i) For any given consumer of X and Y, what will his/her indifference curves look like? Clearly show the direction of preference. (ii) Suppose now, that good X becomes costly and is priced (by regulation) at PX = 170 per unit. A firm that wishes to sell commodity X in the market faces a total cost of TC = 100 + 10X + 16X2, which indicates that his marginal cost function is...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
Sally consumes two goods, X and Y. Her utility function is given by the expression U = 2 · XY ^2 . The current market price for X is $10, while the market price for Y is $12. Sally’s current income is $900. a. Sketch a set of two indifference curves for Sally in her consumption of X and Y. b. Write the expression for Sally’s budget constraint. Graph the budget constraint and determine its slope. c. Determine the X,Y...
A firm is selling two goods, A and B, with a total profit function: TP=-16 + 598.8A- 0.3A^2 + 498.5B - 0.2B^2 -0.2AB Find the values of A and B that will maximise profit. Prove that profit is a maximum.
6. The profit function of a firm is (x,y) = px +qy-ar? - By?, where p and q are the prices per unit and ar? + By are the costs of producing and selling x units of the first good and y units of the other. The constants are all positive. (a) Find the values of x and y that maximize profits. Denote them by x* and y'. Verify that the second-order conditions are satisfied. (1) Define (p, q) =...
A price-taking and profit-maximizing firm produces one output at the rate y> 0 using one input r>0 by way of the production function () , where f(x)竺2x2 . The firm's output sells at the price p >0 while the input is purchased at the price wo (a) (b) (c) Determine the lalue of the input that solves the FONC, and denote it by x (p,w). Is Set up the profit maximization problem. Derive the FONC and SOSC. x(p,w) unique? Explain....