12. Which of the following production function shows decreasing returns to scale? (a) f(r) = min{x1, r2}. 1/4 1/2 (b) f(x) = rf + x* %3D 1/4 1/2 (c) f(z) = 11 +r . (d) f(x) = VIj +a3.
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- Assume that it costs a company approximately C(x) = 400,000 + 160x + 0.002x2 dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- v than the average cost from (b). This means that the average cost is ---Select--- v at a production level of 10,000 smartphones. Need Help? Watch It(a) Find the marginal cost function C'(x). C'(x) Use it to estimate how fast the cost is increasing when x = 60,000. | per game system Compare this with the exact cost of producing the 60,001st game system. The cost is increasing at the rate of $ | game system is $| the estimated cost of producing the 60,001st game system found using the marginal cost function. | per game system. The exact cost of producing the 60,001st J. The actual cost of producing the 60,001st game system is --Select-- (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (Round your answer to the nearest cent.) C(x) C(60,000) - $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.Assume that it costs a company approximately C(x) = 400,000 + 180x + 0.001x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.
- The total cost (in dollars) of producing x food processors is C(x) = 1600 + 40x-0.1x². (A) Find the exact cost of producing the 61st food processor. (B) Use the marginal cost to approximate the cost of producing the 61st food processor. CHEO (A) The exact cost of producing the 61st food processor is $ (B) Using the marginal cost, the approximate cost of producing the 61st food processor is $Q5 A firm makes beer and its cost function is C(q) = 4+q². Are there economies of scale?A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?
- Assume that it costs a company approximately C(x) = 400,000 + 140x + 0.003x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 400,000 – 0.000009 Use it to estimate how fast the cost is increasing when x = 10,000. 2$ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. -Select--- at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- than the average cost from (b). This means that the average cost isProduction function of a company is given by f(x;y)= root of x + root of y where x is labor and y is capital. Cost of labor is 2 currency units, while the cost of capital is 1 currency unit. What are the minimal cost to produce 10 units of the product? What is the change in the costs, if the production volume would increase by 50 %?Suppose that the cost function for a commodity is C(x) = 40 + x2 dollars. (a) Find the marginal cost at x = 4 units. MC(4) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 5th unit is predicted to be $ (b) Calculate C(5) – C(4) to find the actual cost of producing 1 additional unit. Need Help? Read It Watch It
- Cost (thousands of $) The graph shown on the right represents the cost C (in thousands of dollars) of refining x gallons of gasoline per hour (in thousands). The vertical axis represents the cost, and the horizontal axis represents the number of gallons of gasoline refined. Cost of refining gasoline per hour 1000- 800- 600- 400- Answer the following questions below in parts (a) through (d). 200 O 100 200 300 400 500 600 700 800 Number of Gallorns (thousands) (a) What is the cost of refining 200 thousand gallons of gasoline per hour? thousand2. What is the relationship between the total cost curve, and the average cost per unit? Explain their relationship, and draw a diagram showing how the two are related. The total cost of production, in thousands of dollars, is C(q) = q³ 12q² + 60q, where q is in thousands and 0 ≤ q ≤ 8. (a) Graph C(q). Estimate visually the quantity at which average cost is minimized. (b) Determine analytically the exact value of q at which average cost is minimized.It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake issold for $4.90 each.(i) Make a table showing the total cost and the revenue obtained from producing 20,40,60,80 and 100 cupcakes.(ii) Write algebraic expressions representing the cost C and the revenue R as functions of the number of cupcakes X produced and number of cupcakes X sold respectively.(iii) Graph both functions on the same coordinate axes and from your graph determine the cordinate at which cost equals revenue.