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- 1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?For the cost function C(Q) = 100 + 2Q + 3Q², the total variable cost of producing 2 units of output is Multiple Choice о 16. 10. 4. 12.Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.
- Yummy Gummies, Inc. makes boxes of individually packaged gummies. The company has a cost function given by C(x) dollars when x boxes of Yummy Gummies are made. If C '(100) = $3.50 per box, which of the following can we conclude from this information? %3D O The approximate cost of making the 100" box of Yummy Gummies is $3.50. O The exact cost of making the 99h box of Yummy Gummies is $3.50. The approximate cost of making the 101“ box of Yummy Gummies is $3.50. O The approximate cost of making the 99 box of Yummy Gummies is $3.50. O The exact cost of making the 101st box of Yummy Gummies is $3.50.Suppose that the dollar cost of producing x appliances is c(x) = 1000 + 70x-0.1x². a. Find the average cost per appliance of producing the first 100 appliances. b. Find the marginal cost when 100 appliances are produced. c. Show that the marginal cost when 100 appliances are produced is approximately the cost of producing one more appliance after the first 100 have been made, by calculating the latter cost directly. CUCKO The average cost per appliance of producing the first 100 appliances is $ (Round to the nearest cent as needed.) /appliance.Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)
- Consider the following cost function: C= 0.25q - 49° + 85q + 150: When output is 16 units, average cost is $ (Enter a numeric response using a real number rounded to two decimal places.) When output is 16 units, marginal cost is $ The output level where average variable cost equals marginal cost is units. 20 tv MacBook Air 80 DII F2 F3 F4 FB F10 F11 %23 $ & 3 4 5 8 { [ ン E R Y U P D F G K C V N M command option .. .. トSuppose that the cost function for a commodity is C(x) = 90 + x? dollars. (a) Find the marginal cost at x = 7 units. MC(7) = [ Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 8th unit is predicted to be $ (b) Calculate C(8) - C(7) to find the actual cost of producing 1 additional unit. $4Assume 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.
- Suppose that the dollar cost of producing q appliances is c(q) = 1500 + 140q-0.3q. (a) Find the average cost per appliance of producing the first 150 appliances. (b) Find the marginal cost when 150 appliances are produced. (a) The average cost per appliance of producing the first 150 appliances is $ (Round to the nearest cent as needed.) per appliance. The total-cost function for an electric light and power plant is estimated to be c= 32.07 -0.79g +0.02142q -0.0001g 10sqs 100 where q is the eight-hour total output (as a percentage of capacity) and c is the total fuel cost in dollars. Find the marginal-cost function and evaluate it when q 38. Determine the marginal-cost function. Select the correct choice below and fill in the answer box to complete your choice. (Use integers or decimals for any numbers in the expression.) OA. dq OB.The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviar sells for 300 SEK per kg. In bad weather it sells for only 200 SEK per kg. Caviar produced one week will not keep until the next week, i.e. it has to be sold and consumed the same week it is produced. A small caviar producer has a cost function given by C=5q2 - 50q + 1000 where q is the weekly caviar production. Production decisions must be made before the weather (and hence the price of caviar) is known, but it is known that good weather and bad weather each occur with a probability of 0.5. a) How much caviar should the firm produce per week if it wishes to maximise its expected profit? b) Suppose the owner of the firm has a utility function of the form U(π)=√π where π is weekly profits. What is the expected utility associated with the strategy in (a)? c) Suggest a weekly production level that would give the owner higher expected utility than the…E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy
