I believe this is asking us to do a partial derivative. I will include the questions below. As well as you'll see some of my work. If I'm able to complete this section, I should be able to do the rest.
Yuri’s Meat Market competes with Zelda’s Butchery in the market for eight-ounce steaks. Yuri’s demand function is$ Q_Y (P_Y,P_Z )=200-10P_Y+P_Z$, while Zelda’s is $Q_Z (P_Z,P_Y )=223-10P_Z+P_Y$. Yuri’s marginal cost per eight-ounce steak is $\$4$, while Zelda’s is $\$5$.
Suppose $P_Z$ is $10$. Derive an expression for Yuri’s own-price demand elasticity in terms of $P_Y$. (Recall: $ε_P=Q^{'}(P)\cdot \frac{P}{Q(P)}$ , which you can find after plugging Zelda’s price in.) We know for Demand:
$Qy(P_Y, P_Y) = 200 – 10P_Y + P_Z$
$Q_Z(P_Z, P_Z) = 223-10P_Z + P_Y$
We know Marginal cost is: $MC_Y = 4$, $MC_Z = 5$
Now we solve for Yuri’s price elasticity: $ε_Y=$
Now repeat with supposing $P_Z$ is $\$15$.
Does Yuri’s demand become more or less elastic when Zelda raises their price?
What is the nash equilibrium?