You are the Economic Consultant for Zuku Farms Ghana Limited. Zuku produces cowpea in a community where producers are able to switch back and forth between cowpea and groundnut depending on market conditions. Consequently, you were tasked by the management of Zuku and you estimated the demand function for cowpea as follows: Q_d = 1000 - 9.5P_c + 16.2P_g + 0.2Y

where Q_dis the quantity of cowpea demanded in bags per month, P_cis the average price of cowpea in Ghana Cedis, P_gis the average price of groundnut in Ghana Cedis, and Y is the income of consumers.

a. Assumingis initially GH31.00 per bag, Y is GH1001.50

i. Find the resulting demand function for cowpea and determine the number of bags Zuku can sell at GH 45.00 per bag.

ii. Management is considering increasing price of cowpea by GH10.00 per bag. Advise management on this price change using the concept of price elasticity of demand.

iii. Explain why management should be worried about a reduction in the price of groundnut.

Assume also that your estimated supply function for cowpea as follows:

Qs= -25 + 3.5P_c - 1.5P_f - 0.5P_g + 0.25R

Where Q_sis the quantity supplied of cowpea in bags, P_sand P_gare as defined above, P_gis the price of fertilizer per bag,R is the amount of rainfall (in inches).

If P_f=GH10 , R=40inches and P_g= GH31.00.

b. Find the resulting supply function for cowpea and determine the equilibrium price and quantity.

c. Assuming the government imposes a tax of GH10 on every bag of cowpea sold, determine the new equilibrium price and quantity. Explain the effect of the policy on the market.

d. Sketch the demand curve and the supply curves for cowpea.