Consider the following model for the production of refined oil: MSC = 10 +0.5Q; MEC = 0.30: MSB=30-0.3Q; MEB = 0. Based on the model, the MPC function is: MPC20-0.8Q a. MPC 10+ 0.8Q 10+ 0.2Q b. MPC30-0.6Q MPC C. d.
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- Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)Find MPC if MPS = 0.8The Nike accounting firm analyzes the price-demand relationship toconclude that x thousand shoes will sell if offered for a unit price (in dollars) of p(x) = 130−0.1x. Suppose further that the total cost of production was tracked to be $530,000 up until production of the first thousand shoes, and that this cost increased linearly to $560,000 by the time of production ofthe 2000th shoe. Find the following quantities, and interpret your results(describe what these quantities represent). a) Marginal revenue when x= 100 b) Average profit when x= 500
- A small company produces organic cookies. When the price is $6 per dozen, the average daily sales has been 72 dozen cookies. When the price was decreased to $3 per dozen, the average daily sales increased to 110 dozen cookies. Assume that daily cookie sales is linearly related to price per dozen. Each dozen cookies has a variable cost of 87 cents to make, plus additional daily fixed costs of $84. Find a function that models the daily profit in terms of the sales x in dozens of cookies.Bounds Inc. determined through regression analysis that its sales (S) are a function of the amount of advertising (measured in units) in two different media. This relationship is given by the following equation (X = newspapers, Y = magazines): S (X, Y) = 200X+100Y− 10X2− 20Y2 + 20XY Find the level of newspaper and magazine advertising that maximizes the firm’s sales. Calculate the firm’s sales at the optimal values of newspaper and magazine advertising determined in part (a).AVC=10-0.03Q + 0.00005Q2TFC=60What is the TC function?What is the minimum AVC?
- A U.S. electronics firm is considering moving its production abroad. Its production function is: q=L = L 0.50 0.50 (based on Hsieh, 1995), so MPL = 0.5q/L and MPK = 0.5q/K. In the United States, w=$10=r. At its Asian plant, the firm will pay a 10% lower wage and a 10% higher cost of capital: w* = $9.09 and r* = $11.00. What are L and K and what is the cost of producing q= 100 units in both countries? (for all responses, enter a real number rounded to two decimal places) In the U.S., L is 100, K is 100, and the cost of production is $ 2000 In Asia, LisThe demand function for a tablet is given by the model P= 200-16x2 where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derive when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?The demand function for a product is given by P = 4000/ln (x+10), where P is the price per unit in dollars when x units are demanded.i. Find the rate of change of price with respect to the number of units sold when 40 units are sold ii. Find the rate of change of price with respect to the number of units sold when 90 units are sold.iii. Find the second derivative to see whether the rate at which the price is changing at 40 units is increasing or decreasing.
- Given that the C = 600 + 0.1Y and Y = 8000 find the level of the consumptionAVC=10-0.03Q + 0.00005Q2TFC=60What is the output where AVC is minimum?Suppose the relationship between your study time and your grade on a History midterm is given by the following table: If you study for Your grade will be 4 hours 80 5 hours 90 6 hours 93 a) What is the "marginal grade improvement (MGI)" of the 5th hour of studying? b) What is the "marginal grade improvement (MGI)" of the 6th hour of studying? c) Why might the MGI be diminishing?