Question

Homework Questions: Problem #1: Elasticity. Demand and Sunnly and Modeling Competitive Markets (0 points) One of the more useful applications of an elasticity is the ability to determine supply and dema ply and demand curves using the elasticity and one other point along the demand or supply curve, usually the equilibrium point. This property of elasticities makes them very useful in constructing economic models, because we usually only have one data point for a given year when conducting economie analyses using supply and demand curves. Here is how the construction of the supply and demand curves is accomplished. First, assume that the demand and supply equations take the following form: (1) Demand Curve: (ii) Supply Curve: Q =a +bP, and Qs =c+dP, where a and care intercept terms and b and dare slopes for the demand and supply curves. Now. given the equilibrium point (Q*,P) we can determine what b and d are by utilizing the following formulas: (iii) b=19, and P. (iv) d = 0 where is the equilibrium quantity, Pis the equilibrium price, n is the elasticity of demand, and is the elasticity of supply. Now that we have determined b and d we can use the equilibrium point and the two slope coefficients to solve for a and c using the following formulas: (v) a = 2*-bP, and (vi) c = -dP After obtaining, a, b, c, and d we can then graph our supply and demand curves and use them for graphical and analytical analysis. Consider the market for chickens in the United States. Assume that the elasticity of demand for chickens is n = -1 and the elasticity of supply for chickens is e=0.5. Furthermore, assume that the equilibrium in the chicken market is at (Q.P*) (10.5). Derive the demand and supply equations using the process discussed above. Place your answers in the spaces provided below. (2 points) d-

This is all i was given for the problem. Can anyone help me?

Answer 1

Given : $\eta$=-1 , $\varepsilon$=0.5 , P* = 5 , Q* = 10

Then, b = $\eta$*Q*/P* = -1*10/5 = -2

and d = $\varepsilon$*Q*/P* = 0.5*10/5 = 1

Now, a=Q*-bP*

or, a = 10+2*5 = 20

and c = Q*-dP*

or, c = 10-1*5 = 5

Then, Demand curve is Q_d=a+bP

or, Q_d=20-2P

For the demand curve, when P=0, Q_d=20 and when Q_d=0, P=10. Thus, demand curve has horizontal and vertical intercepts of 20 and 10 respectively.

and Supply curve is Q_s=c+dP

or, Q_s=5+P

For the supply curve, when P=0, Q_s=5 ; when Q_s=0, P=-5 and when P=5, Q_s=10. Thus, supply curve has horizontal and vertical intercepts of 5 and -5 respectively and passes through point (10,5).

Price Supply 10 5 Demand Quantity 5 10 20 O