Question

4.2. The following information for the maize market is given:
Supply curve equation: QS = 1 650 + 230P (quantity supplied can, of course, never be negative)
Demand curve equation: QD = 3 250 – 256P
4.2.1. Calculate the equilibrium price and quantity from the given equations. (Hint: At equilibrium, QS = QD. Use this information to calculate the equilibrium price P and then substitute the value of P into either one of the equations to obtain the equilibrium quantity Q.) (4)
4.2.2. Calculate the price elasticity of supply for maize at equilibrium. (2)
4.2.3. Calculate the price elasticity of demand for maize at equilibrium. (2)
4.3. Consider two goods X and Y. The price of product X increases from R8 to R10 per unit. As a result, the quantity demanded of product Y decreases from 220 to 205 units.
Given the information above, calculate the cross-price elasticity of demand by indicating and using the midpoint (arc) formula.

Answer 1

Given, Qd = 3250 - 256P

Supply function, Qs = 1650 + 230P

1. Equating quantity demanded to supply we get

3250 - 256P = 1650 + 230P

=> 230P + 256P = 3250 - 1650

=> 486P = 1600

=> P = 1600 / 486 = $ 3.29 / unit

Q = 1650 + 230P = 1650 + 230 × 3.29 = 2,407 units (Approximately)

2. Price elasticity of supply can be measured using the following formula

Es = %∆ Q /%∆ P

=> Es = (dQs/dP) ×(P/Qs)

Supply function is Qs = 1650 + 230P

Differentiating supply function wrt P we get

dQs /dP = 230

Plug in the calculated values in the equation of elasticity

Es = 230 × (3.29 / 2407) = 0.3144

3. Price elasticity of demand can be measured using the following formula

E = %∆ Q / % ∆ P

=> E = (dQ/dP) ×(P/Q)

Differentiating the demand function we get

Q = 3250 - 256P

=> dQ/dP = - 256

Plug in this in the formula of elasticity

E = (-256)×(3.29 / 2407)

=> E = - 0.3499 (Inelastic)

4.3. price of good X increases from R 8 to R 10. Then quantity of Y changes from 220 to 205.

The cross elasticity of demand can be measured using the following formula

Applying mid point method we get

Om simplifying we get

Plug in the values in the equation we get

Cross elasticity = - 0.3176 (Complement)

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