Chapter $18$ Homework

$6.$ Using a payoff matrix to determine the equilibrium outcome

Suppose that Vitablend and Blend Magic are the only two firms in a hypothetical market that produce and sell personal blenders. The following payoff matrix gives profit scenarios for each company $($in millions of dollars$),$ depending on whether it chooses to set a high or low price for blenders.

$\backslash$table$[[$Vitablend Pricing,,Blend Magic Pricing$],[,$High,Low$],[$High$,14,14,5,21],[$Low$,21,5,13,13]]$

For example, the lower$-$left cell shows that if Vitablend prices low and Blend Magic prices high, Vitablend will earn a profit of $$21$ million, and Blend Magic will earn a profit of $$5$ million. Assume this is a simultaneous game and that Vitablend and Blend Magic are both profit$-$maximizing firms.

If Vitablend prices high, Blend Magic will make more profit if it chooses a low $$ price, and if Vitablend.prices low, Blend Magic will make more profit if it chooses a low $$ price.

If Blend Magic prices high, Vitablend will make more profit if it chooses a low grad price, and if Blend Magic prices low, Vitablend will make more profit if it chooses a price.

Considering all of the information given, pricing low $q,$ a dominant strategy for both Vitablend and Blend Magic.

If the firms do not collude, what strategies will they end up choosing?

Both Vitablend and Blend Magic will choose a low price.

$$ Both Vitablend and Blend Magic will choose a hiah price.