# Task 3. Maximum 20 points

Consider a consumer who plans to use a coffee machine. Let's assume the consumer lives for two periods and values the benefit of using the coffee machine at 10 monetary units in each period. Coffee machines can be produced in two types: durable, working for two periods, and low-quality, completely breaking down at the end of each period. It is known that the technology for producing durable machines allows them to be produced with constant average costs of 6 monetary units. Low-quality coffee machines can be produced with constant average costs of C monetary units.

(a) Suppose coffee machines are produced only by a monopoly. For what average costs C will the monopoly produce only durable coffee machines?

(b) How would your answer to part (a) change if coffee machines of both types are produced in a perfectly competitive market?

(c) What conditions for choosing the lifespan of a coffee machine have we not considered? Come up with at least one and explain how its inclusion in the model would affect the choice in the conditions of part (a) and part (b).
# Solution and Grading Scheme:

(a) When coffee machines are produced by a monopoly, it sets a selling price that will extract all consumer surplus:

1) when producing a durable machine, the price equals the consumer's benefit from using the coffee machine for 2 periods $\mathrm{p}_{\mathrm{L}}=2 \cdot 10=20$ (1 point)
2) when producing a low-quality coffee machine, the price will be equal to the benefit from using it for one period $\mathrm{p}_{\mathrm{s}}=10 .(\mathbf{1}$ point)

Calculate the profit from producing a durable machine: $\pi_{\mathrm{L}}=20-6=14$. ( $\mathbf{1}$ point)

Profit from producing a low-quality coffee machine: $\pi_{\mathrm{S}}=10$ - c. ( $\mathbf{1}$ point)

For the monopolist to find it profitable to produce a durable machine, the profit from its production must be greater than the profit from producing two low-quality machines (since the service life of the durable one is twice as long):

$$
14>2(10 \text { - c) (2 points) }
$$

From this, it follows that c $>3$. ( $\mathbf{1}$ point)

(b) In this case, coffee machines will be sold at prices equal to the costs of their production: $\mathrm{q}_{\mathrm{L}}=6$ and $\mathrm{q}_{\mathrm{s}}=\mathrm{c}$. (2 points) For only durable machines to be produced, it is necessary that consumers prefer to buy only them.

The net consumer surplus from buying a durable machine will be $2 \cdot 10-\mathrm{q}_{\mathrm{L}}=20-$ $6=14$. ( 2 points)

The net consumer surplus from buying two low-quality coffee machines will be $2\left(10-\mathrm{q}_{\mathrm{s}}\right)=2(10-\mathrm{c}) .(\mathbf{2}$ points)

Thus, the decision to buy only durable machines will be made if the inequality $14>2(10-$ c) and c $>3$ is satisfied, i.e., the answer does not change. ( $\mathbf{1}$ point)

(c) costs of purchasing (going to the store, searching online - can vary over two periods), costs of disposing of a broken coffee machine (need to recycle it), etc. You need to demonstrate how the inequalities change with the addition of this new condition. (6 points)