.Answer these attachments.
10. EQUILIBRIUM (10 POINTS) The market demand function for widgets is QD = 100 2PD+10M where Q D denotes the quantity demanded, PD denotes the price of widgets, and M denotes income. The market supply function for widgets is Q3 = 50+ 6P5 30'2 where Q5 is the quantity supplied, P3 is the price producers receive for selling widgets, and C is the cost of material used to produce widgets. (a) (2 POINTS) Write down the equation that you would solve to nd the equilibrium price in the market for widgets. (b) ( 3 POINTS) Solve the equation that you wrote down in Part a to express the equilibrium price as a function of the exogenous variabies. Label your solution P\". (c) (3 POINTS) Use your answer from Part b to solve for the equilibrium quantity in the market as a function of the exogenous variables. Label your solution Q\". (d) (2 POINTS) Using your answer from Part b, calculate (332... How does an increase in C affect the equilibrium price in this model? Each firm produces both goods, i.e., good 1 and good 2. Each firm takes the market prices p1 2 0 and p2 2 0 as given and chooses output to maximize profits. If a firm produces x1 units of good 1 and 2 units of good 2, with (21, 12) E R?, it has the total costs of C(1, x2) = 3+0.523 1200 (a) (1 point ) For given prices p, and p2, find the revenue, R($1, 12), of a single firm. (b) (1 points) Find the profit function, II(21, 12), of a single firm. (c) (10 points) Solve the profit-maximization problem, that is, derive the system of first-order conditions and solve this system. That is, find the critical point of II. Your solution might depend on p, and on p2.146 Part 2 Consumption and Production probably look like? Explain your reasoning by ence curve that reflects Cheryl's situation. What drawing a graph that includes her indifference curves must ber indifference curves look like? and a hypothetical budget constraint. C. Suppose Cheryl receives a gift of one ugly 21. Economist Joel Waldfogel may be America's biggest sweater from a coworker. Show the effect of the Grinch. He bemoans what he calls the "deadweight gift on Cheryl's budget constraint. Where on the loss of Christmas" created when people give gifts constraint is Cheryl likely to maximize her utility? (such as ugly sweaters) the recipients would rarely. d. Waldfogel suggests that the world might be a if ever, buy for themselves. happier place if instead of giving ugly sweat- a. Draw a graph with a budget constraint showing ers, people simply gave an equivalent amount of affordable bundles of a composite good costing cash. Draw the budget constraint Cheryl would $1 and ugly sweaters. (You may assume some face were this the case. Add an indifference curve level of income and a price for ugly sweaters.) or two to show what happens when Cheryl maxi- h. Cheryl might get some utility from an ugly mizes her utility. Does the cash gift make her sweater, but is currently spending all of her in happier than the sweater? come on the composite good. Add an indiffer-Beaker 0.002 M NaSCN 0.200 M Fe(NOg)3 Equal in 0.1M HNOg (mL) In 0.1 M HINOg (mL) 0.1 M HNO (mL] 0.0 0.1 2.5 2.5 7.5 0.2 2.5 7.4 0.4 2.5 7.3 0.6 2.5 7.1 0.8 2.5 6.8 1.0 2.5 6.7 6.5 3. Set the spectrophotometer to 447 nm (the wavelength of maximum absorption). Without a test Of tube in the sample holder, adjust the zero transmittance. two 4. Pour some of the solution from beaker 1 into your cuvette, and use this to set the 100% trans- mistance. You should note that solution I has no SCN, thus is pure, yellow Fel. By setting the We 100% transmittance to this, you are effectively subtracting the effect of the Felt from your mea- surements. has 5. Clean the cuvette and then pour some of solution 2 into it and record its transmittance (la). 6. Clean the cuvette thoroughly, and rinse with the next solution. ation 7. Repeat steps 5 and 6 with each of the remaining solutions. 8. Do the appropriate calculations and draw the calibration curve. you B. Collection of Equilibrium Datainvain sayim will 9. In six clean, dry beakers, prepare the following reaction mixtures. Note that the concentration of the Fe(NO,), solution used in this part is much smaller than that used in Part A. Stir for about a di- minute. Beaker 0.002 M NaSCN 0.002 M Fe(NOg)3 0.1 M HNO3 (mL) in 0.1M HNO3 (mL) in 0.1 M HNOg (mL) or- 5 5 4.0 1.0 5.0 2.0 5.0 GOL x 3.0 3.0 5.0 20 1.0 4.0 5.0 0.0 5.0 5.0 10. Recalibrate the 100% transmittance as in step 4 using the new beaker 1, which only contains the hly. Fe(NO ,), solution. M. Rinsing the cuvette before each use with the appropriate solution, measure the transmittance of each reaction mixture (2a)- 12. Carry out the appropriate calculations and determine your average K, (3). 13. Obtain the class data (4) and calculate the class mean (5) and standard deviation (6). 121
