7. In a certain country, the demand function for Moroccan tangerines is $\mathrm{Q}_{\mathrm{d}}(\mathrm{p})=50-\mathrm{p}$, the marginal costs of production and supply of any tangerines are constant and equal to 5, and the tangerine market operates under conditions of perfect competition. An embargo, imposed on tangerines grown in any country other than Morocco, increased the demand for Moroccan tangerines by two and a half times at any price of this product, all other conditions being equal, and Morocco became the only supplier of this fruit in the country. By what factor did the consumption of Moroccan tangerines by the residents of this country change? Illustrate the solution graphically. (9 points)
# Solution:

Before the embargo, there was equilibrium in the competitive market for Moroccan mandarins. The price of the good should be equal to the marginal cost of its production, as the marginal revenue of any supplier is equal to the price of the good. Therefore, Moroccan mandarins were consumed in a volume of $\mathrm{Q}_{\mathrm{d}}(5)=50-5=45$.

After the embargo was imposed, the demand for mandarins increased by 2.5 times and is given by $Q^{\text {new }}{ }_{d}(\mathrm{p})=2.5(50-\mathrm{p})=125-2.5 \mathrm{p}$, and the supplier becomes a monopolist in the market. The inverse demand function for Moroccan mandarins is $\mathrm{P}_{\mathrm{d}}(\mathrm{Q})=50-0.4 \mathrm{Q}$.

The profit of the monopolist is given by $\Pi=(50-0.4 Q) Q-5 \mathrm{Q}$. Graphically, the curve representing this function is a parabola with its branches pointing downwards, so the maximum profit is achieved at $\mathrm{Q}=56.25$.

Therefore, the consumption volume of Moroccan mandarins increased by 56.25/45=1.25 times. Let's illustrate the solution graphically:

![](https://cdn.mathpix.com/cropped/2024_05_06_1de37bea369d17028379g-07.jpg?height=739&width=1333&top_left_y=1401&top_left_x=287)

## Grading Criteria:

Correctly found the equilibrium sales volume before the embargo - 2 points

Correctly found the demand function after the embargo - 1 point

Correctly found the equilibrium sales volume after the embargo - 2 points

Correctly found the factor by which sales volume changed - 1 point

Correctly graphically illustrated the solution - 3 points