Determine whether each firm has a dominant strategy.

$(4$ marks$)$

ii$)$ Find the Nash equilibrium in this game.

$(3$ marks$)$

iii$)$ Can you describe this game as an example of the prisoners' dilemma? Explain.

$(3$ marks$)$

iv$)$ If Firm A could move first, determine sequential, the optimal strategy.

$(4$ marks$)$

b$)$ Anna is employed by a manufacturing company, but because of the predictions of low economic growth and high inflation from the end of $2022$ to $2023,$ is unsure if she will keep her job. Her income $)$ from her current job is R$90,000.$ There is an $80\%$ probability that she will keep her job and earn this income. However, there is a $20\%$ probability that she will be laid off and will be out of work for a long time. The lay$-$off will force her to accept a lower$-$paying job. In this case, her income is R$10,000.$

Show that Anna's expected value of her income is thus $\mathrm{????}74,000.$

If Anna$`$s utility function has the formula $100\mathrm{????}-0\mathrm{.}0001\mathrm{????}2$

i$)$ Determine the value of the insurance required to the purchase insurance policy

ii$)$ Interpret the value in $($i$).$

QUESTION $3$

Suppose you are a consultant working for an economic advisory company which is working on an assignment in the electric car battery manufacturing industry using Lithium. The client has provided your manager with the information needed to complete the assignment. The market demand curve in the lithium electric car battery manufacturing industry is given $\mathrm{????}=200-2\mathrm{????}.$ The industry is dominated by a large firm with a marginal cost of $\mathrm{????}4$ per kilogram. There is a competitive fringe of $12$ pricetaking firms, each of which has a total cost function $\mathrm{????}\mathrm{????}=3\mathrm{????}2+20\mathrm{????}.$ To complete the report your manager requires the information below.

a$)$ Find the supply function of the fringe firms.

$(3$ marks$)$

b$)($i$)$ Find the output and price of the dominant and fringe firms.

$(3\mathrm{.}5$ marks$)$

$($ii$)$ Find the dominant firm's profit, markup and elasticity of demand. $(3\mathrm{.}5$ marks$)$

c$)$ Graph your answer to part $($b$).$

$(4$ marks$)$

d$)$ Calculate the welfare effects of a dominant firm.

$(2$ marks$)$

e$)$ Determine the effects on dominant and fringe when

$($i$)$ the total market demand doubles.

$(3\mathrm{.}5$ marks$)$

$($ii$)$ the marginal costs double

$(3\mathrm{.}5$ marks$)$

f$)$ Give a recommendation based on results in b$)$ and e$).$