Firms need to decide the proportion of various inputs they will employ in producing their output in order to either minimize cost or maximize profit. Assume that the maker of Samsung appliances is employing variable resources Capital (X) and Labour (Y) in such amounts that the MRPs of the last units of X and Y employed are $100 and $60, respectively. Resource X can be hired at $50 per unit and resource Y at $80 per unit. The firm Multiple Choice   shut down.   should hire more of both X and Y.   is using the least-costly combination of X and Y but could increase its profits by employing less of both X and Y.   should hire more of X and less of Y.   is producing with the least-costly combination of X and Y but could increase its profits by employing more of X and less of Y.

2. Consider the following information of a hypothetical firm: Q = 100K0.6 L0.8, w = = 1; r = 3 A. Solve for the cost-minimizing quantity of capital (K*) and labor (L*), and the minimum cost (C*) if the firm targets to produce 3,000 units of output. (10 pts) B. If target output increases to 6,000 units, solve for the new cost-minimizing quantity of capital and labor, and the minimum cost. (10 pts) C. Graphically illustrate the expansion path for the firm if it decides to increase its target output from 3,000 units to 6,000 units. (10 pts)

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(This is a single question with five parts to the answer. I would appreciate help with all five parts if possible. Image screenshot of the original question with the formulas more easily readable than can be identified here is attached) Tech firms produce goods and services from labor and energy. The total cost in dollars to produce y amount of goods and services for each firm j is cj(yj) = yi2. There are 100 identical tech firms which all behave competitively. What is the individual supply of technological goods and services?  What is the market supply of technological goods and services? Suppose the demand curve for these goods is D(p)=200-50p. What is the equilibrium price and quantity sold? How much is the total surplus of this economy?  Now suppose that the industry makes a one-time investment for $K amount of dollars to innovate in a new technology of production that allows every firm to reduce its cost of production to a 1/4 fraction of the previous cost. What is the new total…

Please answer in detail according to the picture. Show that the cost function is homogeneous of degree 1/(α+β) in output. How do the returns to scale (degree of homogeneity of the production function) relate to the propertiesof the cost function? Does this make sense to you? Explain clearly why.

The short run production function of a competitive firm is given The short-run production function of a competitive firm is given by f (L) = 6L2/3, where L is the amount of labor it uses. (For those who do not know calculus—if total output is aLb, where a and b are constants, and where L is the amount of some factor of production, then the marginal product of L is given by the formula abLb−1.) The cost per unit of labor is w = 6 and the price per unit of output is p = 3. (a) Plot a few points on the graph of this firm’s production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0, 8), and the isoprofit line that passes through the point (0, 4). What is the slope of each of the isoprofit lines? (b) How many units of labor will the firm hire? (c) Suppose that the wage of labor falls to 4, and the price of output…

Assume that the production function for competitive firm is given by F(L)=9L1/3, where L is the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?

A competitive firm’s production function is given by y= f(x1,x2)=x1ax2b   If a=b=0.5 , the price of factor 1 is 12, and the price of factor 2 is 3, find the cost minimizing input combinations and the total cost of producing 40 units of output. Redo part (1), this time by first deriving the firm’s conditional factor demand functions and the cost function.