Microeconomics. Thanks.

Start with the spreadsheet you developed for Chapter 5. 1. Assume total Fixed Costs are $15 and add a column labeled Fixed Costs. 2. Calculate Average Fixed Costs (AFC) by dividing total Fixed Costs by output (y), and add a column labeled AFC. 3. Calculate Total Cost by adding your old Total Factor Cost column to the column you created for FC. 4. Now define AVC as the price of the input (x) divided by the APP of the input. That is, AVC = w/APP, and add a column for AVC. 149 Applied Microeconomics 5. Now define MC as the price of the input x divided by the MPP of the input. That is, MC = W/MPP and add a column for MC. 6. Now make a column in which you have added AVC +AFC and label that AC. Make the following graphs. Be sure to plot these with output (y) not input (x) on the horizontal axis. 1. Plot TVC (which is actually TFC but with y not x on the horizontal axis). Also plot FC and TC on the same graph. 2. Plot AVC, AFC, and AC again with y not x on the horizontal axis. Plot MC and MR with y on the horizontal axis.Suppose that the equation for a demand function is given by P = A +b*Q., and the supply function is given by P= C + d*Q. Further, at equilibrium, Q. = Qs = Q. That is, the market is cleared. Again assume that A = 40, b = -2, C = 0, d = 1.5 and that Q. = quantity demanded, and Q = quantity supplied. Assume that quantity goes from 0 to 20 in 1 unit increments. The formula for calculating the elasticity of demand at any of the points along the demand function is (dQa/dP)*(P/Qa). Note: do./dP is the inverse slope of the demand function and is not the same as dP/dod, which is the slope of the demand function. Specifically note that do./dP= 1/(dP/dQ.). For example, if the slope of the demand function is -2, what is the inverse slope of the demand function? 1. For the each incremental quantity from 0 to 20, on the spreadsheet, calculate the elasticity of demand. 2. Are all these elasticities negative? Why? 3. Do the points along the demand function become more or less elastic as you move from left to right along the demand function? 4. At what quantity demanded is the elasticity of demand exactly unitary, or -1? Next, assume that the demand function makes a parallel shift outward. You can do this by assuming the parameter A is 50 rather than 40. 56 Elasticities 1. Recalculate the demand elasticities for the same Q. values assuming the parallel shift. 2. For each quantity demanded, are the new elasticities more or less elastic? Now calculate the elasticity of supply. The formula for this is (dos/dP)*P/Qs. Once again, remember that the SLOPE of the supply function is dP/do,, not do./dP. 1. If the slope of the supply function is 1.5, what is the value for the inverse slope of the supply function? 2. Calculate the elasticity of supply for values of Q, from 0 to 20. 3. As you move from left to right along the supply function, does the Supply become more or less elastic? Now assume a demand function of the form Pd = 100.". Calculate the elasticity of demand for this function for values of Q. between 0 and 20. Is the elasticity of demand the same everywhere along this demand function?Spreadsheet Exercise Suppose that the equation for a demand function is given by P = A +b*Q., and the supply function is given by P= C + d*Q. Further, at equilibrium, Q. = Qs = Q. That is, the market is cleared. Again assume that A = 40, b = -2, C = 0, d = 1.5 and that Q. = quantity demanded, and Q. = quantity supplied. Assume that quantity goes from 0 to 20 in 1 unit increments. The formula for calculating the elasticity of demand at any of the points along the demand function is (dQ./dP)*(P/Q.). Note: doa/dP is the inverse slope of the demand function and is not the same as dP/dod, which is the slope of the demand function. Specifically note that do./dP= 1/(dP/dQ.). For example, if the slope of the demand function is -2, what is the inverse slope of the demand function? 1. For the each incremental quantity from 0 to 20, on the spreadsheet, calculate the elasticity of demand. 2. Are all these elasticities negative? Why? 3. Do the points along the demand function become more or less elastic as you move from left to right along the demand function? 4. At what quantity demanded is the elasticity of demand exactly unitary, or -1? Next, assume that the demand function makes a parallel shift outward. You can do this by assuming the parameter A is 50 rather than 40. 56 Elasticities 1. Recalculate the demand elasticities for the same Qa values assuming the parallel shift. 2. For each quantity demanded, are the new elasticities more or less elastic? Now calculate the elasticity of supply. The formula for this is (dQs/dP)*P/Qs. Once again, remember that the SLOPE of the supply function is dP/do,, not doc/dP. 1. If the slope of the supply function is 1.5, what is the value for the inverse slope of the supply function? 2. Calculate the elasticity of supply for values of Q from 0 to 20. 3. As you move from left to right along the supply function, does the Supply become more or less elastic? Now assume a demand function of the form Pd = 100.". Calculate the elasticity of demand for this function for values of Q. between 0 and 20. Is the elasticity of demand the same everywhere along this demand function?Suppose there is a production function representing corn response to nitrogen fertilizer that has been estimated as y= - 0.000023x* + 0.0042x' + 0.75x. 123 Applied Microeconomics where y = Total Physical Product (TPP), that is, yield of corn in bushels per acre. x = pounds of nitrogen fertilizer applied in pounds per acre. For nitrogen levels between 0 lbs and 200 pounds in 10-pound increments, find the yield of corn that is produced Using calculus, determine the exact quantity of nitrogen that maximizes the yield of corn, and note this on your spreadsheet. 1. Graph the TPP function (corn yield on vertical axis and nitrogen application on the horizontal axis) verify the maximum on your spreadsheet. 2. Calculate MPP as the first derivative of his production function. Calculate APP as y/x on your spreadsheet. 3. On a separate chart on your spreadsheet, graph MPP and APP with nitrogen on the horizontal axis. 4. Verify that MPP crosses APP at Maximum APP. 5 . Verify that MPP = 0 at the nitrogen application level that maximizes TPP. Add a column for elasticity of production MPP/APP for each input level. 7 . Verify that the elasticity of production is 1 when MPP = APP and zero when MPP is zero. Now assume that the price of corn is $7 per bushel, and the price of Nitrogen is $1.50 per pound (build your spreadsheet to vary both of these up or down). Add the following columns: VMP = MPP*price of corn. 9. AVP = APP* price of corn. 10. MFC = a constant = the price of nitrogen. 11. TVP = TPP*price of corn or y*price of corn. 12. TFC = price of nitrogen * x. 13. Profit (1) = TVP - TFC. Draw two graphs, one for items 1-7 above, and the other for 8-13 above, putting in the amount of nitrogen (x) used. Verify that the profit-maximizing point occurs at the point where MFC= VMP. Set up the math and use the quadratic formula to determine the exact level of input use that maximizes profit (NOT output) for the firm. Using calculus, determine the exact level of nitrogen use that maximizes profits. Show your calculations on your spreadsheet. Verify that you 124