To find the correct answers to questions 13, 14, and 15, let's analyze the information provided.
Question 13: Demand and Supply Equations
Given:
- Equilibrium price (\(P^*\)) = K40
- Equilibrium quantity (\(Q^*\)) = 250
- Price elasticity of demand (\(E_d\)) = -1.6
- Price elasticity of supply (\(E_s\)) = 0.8
To derive the demand and supply equations, we can use the point-slope form of the equations based on elasticity.
For demand: \[ E_d = \frac{dQ_d}{dP} \cdot \frac{P^}{Q^} \] Where \(E_d = -1.6\), (from here we can find the slope): \[ \frac{dQ_d}{dP} = E_d \cdot \frac{Q^}{P^} = -1.6 \cdot \frac{250}{40} = -10 \] Thus, the demand function can be expressed as: \[ Q_d = Q^* + m_d(P - P^*) \Rightarrow Q_d = 250 - 10(P - 40) \] Resolving it further gives: \[ Q_d = 450 - 10P \]
For supply: \[ E_s = \frac{dQ_s}{dP} \cdot \frac{P^}{Q^} \] Where \(E_s = 0.8\): \[ \frac{dQ_s}{dP} = E_s \cdot \frac{Q^}{P^} = 0.8 \cdot \frac{250}{40} = 5 \] Thus, the supply function can be expressed as: \[ Q_s = Q^* + m_s(P - P^*) \Rightarrow Q_s = 250 + 5(P - 40) \] Resolving further gives: \[ Q_s = 50 + 5P \]
Thus, the equations are:
- Demand: \(Q_d = 450 - 10P\)
- Supply: \(Q_s = 50 + 5P\)
None of the provided options in the question seem to match. So the answer could be: d. None of the above
Question 14: Price Control at K20
Insert K20 into both equations to find quantity demanded and quantity supplied.
For quantity demanded: \[ Q_d = 450 - 10(20) = 450 - 200 = 250 \]
For quantity supplied: \[ Q_s = 50 + 5(20) = 50 + 100 = 150 \]
This implies there will be:
- Consumption = 250
- Production = 150
- Therefore, there is an excess demand (shortage).
So the answer is: b. 368 units, 66 units, shortage (none of the units calculated match this, indicating an interpretation issue).
Question 15: Production Reduction by 30%
If production is reduced by 30%, the new supply at equilibrium price needs to be calculated.
Reduced supply: New \(Q_s = 0.7 \times Original , Q_s\)
Original quantity at K40: \[ Q_s = 150 \text{ (original)} \Rightarrow 0.7 \times 150 = 105 \]
At this supply level, there will be a new price that we have to find by setting \(Q_d = Q_s\).
Substituting \(Q_s\) into the demand equation:
- Given demand remains bring equilibrium around 250,
- Solving for new \(P\) that allow \(Q_d = Q_s\).
None of the options provided can be assessed further without specific reductions.
Thus, the answer could be: d. None of the above
Please note that for precision and exact calculations in economics, you would normally handle these with graphs or computational software, or require more specific information in the options presented to make an accurate identification.