The following regression equations are from the study of the demand for chicken

Question

The following regression equations are from the study of the demand for chicken in the United States for the time period 1960 - 1982. The estimated is given below (t-statistics in parenthesis):

Y = 37.24 + .0050 (X1) - .6104(X2) + .1977 * (X3) + .0693*(X4)

       (9.99)       (1.031)       (3.742)       (3.321)             (1.357)

R2 = .9424

n = 34, k = 5

Y = Per Capita Consumption of Chickens in pounds

X1= Real Disposable Income per capita in dollars

X2 = Real Retail Price of Chicken per pound in cents

X3 = Real Retail Price of Pork per pound in cents

X4 = Real Retail Price of Beef per pound in cents

a. Using this equation suppose you are given the following values of your independent/explanatory variables: X1 = 1165.9; X2 = 58.3; X3 = 123.5; X4 = 142.9. Forecast the value of chicken consumption given the specified values of each X.

b. Calculate the point price elasticity of demand for chicken given the values in part a.

Note: EP = Price Elasticity of Demand

EP = %?Q = ?Q * P

                      %?P     ?P    Q

c. Interpret the elasticity coefficient in part b.

Please show all calculations and complete explanation on how to solve this problem.

Explanation / Answer

a. Y = 37.24 + 0.005X1 - 0.6104X2 + 0.1977X3 + 0.0693X4

Demand of chicken, Y = 37.24 + 0.005*1165.9 - 0.6104*58.3 + 0.1977*123.5 + 0.0693*142.9 = 41.8021 pounds

Value of per capita consumption = Y * X2 = 41.8021 * 58.3 = 2437.062 cents = $24.37062

b. Point elasticity of demand = (Price/Quantity) * (dQ/dP) = (X2/Y)*(dY/dX2).
From the demand equation, Y = 37.24 + 0.005X1 - 0.6104X2 + 0.1977X3 + 0.0693X4 => dY/dX2 = -0.6104
Hence, Point elasticity of demand = (X2/Y)*(dY/dX2) = (58.3/41.8021)*(-0.6104) = -0.851305

c. Point elasticity of demand is -0.851305. This means that quantity demanded of chicken goes down by 0.851305% with every 1% increase in price of the chicken.

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