This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
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Here are the solutions to the demand and supply functions problem: Given the demand and supply functions: Demand function: Q_d = 20 - 2p Supply function: Q_s = 10 + 3p where p is price in cedis and Q is quantity in kilos. i. Determine the equilibrium price and quantity Step 1: Set demand equal to supply to find the equilibrium price. At equilibrium, Q_d = Q_s. 20 - 2p = 10 + 3p Step 2: Solve for p. 20 - 10 = 3p + 2p 10 = 5p p = (10)/(5) p = 2 The equilibrium price is GH¢2. Step 3: Substitute the equilibrium price into either the demand or supply function to find the equilibrium quantity. Using the demand function: Q_d = 20 - 2(2) Q_d = 20 - 4 Q_d = 16 Using the supply function (to verify): Q_s = 10 + 3(2) Q_s = 10 + 6 Q_s = 16 The equilibrium quantity is 16 kilos. The equilibrium price is GH¢2 and the equilibrium quantity is 16 kilos. ii. Calculate point price elasticity of demand at equilibrium The formula for point price elasticity of demand (E_d) is: E_d = (dQ_d)/(dp) × (p)/(Q_d) Step 1: Find the derivative of the demand function with respect to price (p). Given Q_d = 20 - 2p, the derivative (dQ_d)/(dp) is the coefficient of p. (dQ_d)/(dp) = -2 Step 2: Substitute the values of (dQ_d)/(dp), equilibrium price (p), and equilibrium quantity (Q_d) into the elasticity formula. Equilibrium p = 2 Equilibrium Q_d = 16 E_d = -2 × (2)/(16) E_d = -2 × (1)/(8) E_d = -(2)/(8) E_d = -(1)/(4) E_d = -0.25 The point price elasticity of demand at equilibrium is -0.25. iii. Calculate the price elasticity of supply at equilibrium. The formula for point price elasticity of supply (E_s) is: E_s = (dQ_s)/(dp) × (p)/(Q_s) Step 1: Find the derivative of the supply function with respect to price (p). Given Q_s = 10 + 3p, the derivative (dQ_s)/(dp) is the coefficient of p. (dQ_s)/(dp) = 3 Step 2: Substitute the values of (dQ_s)/(dp), equilibrium price (p), and equilibrium quantity (Q_s) into the elasticity formula. Equilibrium p = 2 Equilibrium Q_s = 16 E_s = 3 × (2)/(16) E_s = 3 × (1)/(8) E_s = (3)/(8) E_s = 0.375 The price elasticity of supply at equilibrium is 0.375. 3 done, 2 left today. You're making progress.