The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: π=−10q+2000 $ ( I ) where q is the demand and π is the unit price for this product. A. Determine the maximum consumption of these consumers. B. Determine the price that no consumer is prepared to pay for this product. C. Determine the maximum net consumers’ surplus. Explain why the consumers will not be able to realize this surplus.
The inverse demand function of a group of consumers for a given type of widgets is given by the following expression:
π=−10q+2000 $ ( I )
where q is the demand and π is the unit
A. Determine the maximum consumption of these consumers.
B. Determine the price that no consumer is prepared to pay for this product.
C. Determine the maximum net
D. For a price π of 1000 $/unit, calculate the consumption, the consumers’ gross surplus, the revenue collected by the producers, and the consumers’ net surplus.
E. If the price π increases by 20% (The new price π=1200), calculate the change in consumption and the change in the revenue collected by the producers.
F. What is the price elasticity of demand for this product and this group of consumers when the price π is 1000 $/unit.
G. Derive an expression for the gross consumers’ surplus.
H. The supply function for the widget market is given by the following expression:
q=0.2π−40 ( II )
Calculate the demand and price at the
I. For the equilibrium in H, calculate the consumers’ gross surplus, the consumers’ net surplus, the producers’ revenue, the producers’ profit, and the global welfare.
J. Calculate the effect on the market equilibrium in H of the following interventions:
- A minimum price of $900 per widget
2. A maximum price of $600 per widget
3. A sales tax of $450 per widget.
In each case, calculate the market price, the quantity transacted, the consumers’ net surplus, the producers’ profit, and the global welfare.
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