The Return of Detroit City: Enpar manufactures engine parts for Ford using steel as an input. Enpar operates two plants, one in Detroit, MI and one in Greenville, SC. The production functions for the two Enpar plants are: Detroit: QD=20SD - 0.25 Sp² Greenville: QG= 53SG-0.5 SG² where Qp and QG are the outputs of engine parts (in units) from the Detroit and Greenville plants, respectively. Sp and SG are the amounts of steel for the two plants. The firm has 159 units of steel available

S1. A firm's production function is well described by the equation Input prices are $10 per labor hour and $20 per machine hour, and the firm sells its output at a fixed price of $10 per unit. a. In the short run, the firm has an installed capacity of K = 50 machine hours per day, and this capacity cannot be varied. Create a spreadsheet (based on the example below) to model this production setting. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer. Confirm that MRPL = MCL. C 1 2 3 4 5 6 7 8 9 10 11 12 13 A B Labor MPL Q = 2L .01L² + 3K-.02K². 20.0 1.600 MRPL 16.0 MCL 10.0 D OPTIMAL INPUTS E F Capital 50.0 MPK 1.000 MRPK 10.0 MCK 20.0 G H Output Price MR Revenue Ave Cost I Profit 136.0 10.0 Cost 1200.0 8.8 10.0 1360.0 160.0 b. In the long run, the firm seeks to produce the output found in part (a) by adjusting its use of both labor and capital. Use your spreadsheet's optimizer to find…

Show that the two-input Cobb-Douglas production function (attached) has decreasing return in scale (DRS), constant return of scale (CRS) or increasing return of scale (ITS) depending on if alpha1 + alpha2 is smaller than, equal, or larger than 1.

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How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether β is larger than, smaller than, or equal to one?

Mirtha owns an online jewelry store that specializes in earrings. In March, she sells 50 pairs of earrings priced at $15. The cost of materials to create the 50 pairs of earrings was $100. The website she uses to sell her wares costs her $10 a month, and she is also charged 4% on each sale by the company that processes debit/credit card purchases. Which of the following best represents Mirth’s total cost? Group of answer choices A)The $750 Mirtha earned from earring sales minus the materials ($100), online website charge ($10), and payment processing charge (4%) B)The sum of the materials ($100), website charge ($10), and 4% payment processing charge (4%) C)The cost of all the materials used to create the earrings, $100 D)The costs of materials minus the costs it takes to run her business through the online store, in this case the $10 website charges and the 4% payment processing charge