Question

Is this clearer?

The daily demand for beef can be modeled by 40.007 D(0) = - 1 + 0.03320.354p million pounds where the price for beef is p dollars per pound. Likewise, the supply for beef can be modeled by for p < 0.5 s(p) = {°_ 51 for p > 0.5 (1 + 53.98e-0.395p where S(p) is measured in million pounds and the price for beef is p dollars per pound. (a) How much beef is supplied when the price is $4.50 per pound? (Round your answer to three decimal places.) million pounds Will supply exceed demand at this price? o Yes Ο Νο (b) Locate the point of market equilibrium. (Round your answers to two decimal places.) (p*, q*) = (L. ) (c) Calculate the total social gain from the sale of beef at market equilibrium. (Round your answer to three decimal places.) million

Answer 1

Supply of beef Supply of 5 0 .395 SLP) = 7+53.98 ēron ) p=4.50 51 - 1453.98 0.395x4.50 51 t 53.98 € *7775 51 = 14 153.98)*(0-169) 1 + 90/258 10- 258 /SO) = 5.0366 million pounds At p = $4.50

Demand for beef 40-007 30.3548 OLP) = +0.033e p=4.50 40.007 1+0.033 € 2 0.354x4.5 yo.007 1 +0.033 e!:593 40.007 1+ 0.033)x (4.9184) 40.007 +0.1623 40.007 = 1.1623 P(8) - 34.4202 million pounds At = 4.50 NO, Supply will not exceed demand at $4.50 price

6 market equilibrium will occur when Demand = Supply O(P) = S(p) 51 - 1+53.98 ē 0.3958 40.007 1+ 0.033 0.3548 = 1 40.007 1+53.98 € 0.3930 +0.03300.3568 - 1.27461+0.033 €34P) 2981-D-3950 153 -0.3950 1753.98€ = 1.274 +0.042042 2.5599 -0.395P = 0.276 +0.042042 8.35 53.98 € +0.395 0.356 0-2746 +0.04204205 AP = e 0.3950 53.98 .+49.8 0-3951 = 0. 270 +0.04 2042 53.98

- 0-3950 53.98 -0.276 +0.04 2042 +0.042042 20-7498 de error method trail p = 9:25] DLP= 5(P)- D(0) 40-007 H+ 0.033€0.354X69.25) 40.007 If 0.033* 26.430 40.007 1.87219 pounds at p=9.25 D(P) = S(0) = 21.369 million total gain = 0 (0% 9.25 = 21.369x 9.25 tozal gain(8) – 1 97.663 million