An individual allocates $306$306 each month to buying two goods, X and Y, in such a way that maximizes their utility U(X,Y)=2X12Y12U(X,Y)=2X12Y12. Good X costs $4.25$4.25 and Good Y costs $17$17.

If MUX=Y12X12MUX=Y12X12 and MUY=X12Y12MUY=X12Y12, calculate the substitution and income effect for Good X when the price of Good X falls to $3.40.

Do not round your intermediate calculations, but you can round your final answers for units of X and Y to two decimal places.

A monopolist originally charges one price when producing output for consumers with a market demand function P(Q)=8616QP(Q)=8616Q. Their total cost function is TC(Q)=7,500+8QTC(Q)=7,500+8Q, where MC is constant and equal to $8.

Part (a): When the firm behaves as a single-price monopolist, what is the equilibrium market price and market output level?

Suddenly, the firm discovers that there are actually two groups of consumers in the market. The first group demands the product according to P(q1)=9814q1P(q1)=9814q1, while the second group's willingness to pay can be summarized as P(q2)=6212q2P(q2)=6212q2, where q1+q2=Qq1+q2=Q

Part (b): How much output is sold to each group and what price is charged to each group of consumers?