1. MarketEquilibrium:Consideramarket forvinylrecords wheremarketdemand isgivenby

()=andmarketsupplyisgivenby()=+.

1. Findtheequilibriummarketpriceandquantity sold.

Usingthemodel ofsupply anddemand,whatwouldhappen to the marketifmanyconsumers lost their jobs or had to take reductions in wages/salaries? Illustrate the effect on the market graphically, and discuss how you would expect equilibrium quantity and price to change.

Whatwould happenif,dueto arecent resurgenceinconsumers'interest invinyl,entrepreneurs open up more record pressing facilities to compete with the existing producers? Illustrate the effect on the market graphically, and discuss how you would expect equilibrium quantity and price to change.

What wouldhappenifthepriceofturntables (usedto play vinyl records)falls? Illustrate graphically,anddiscuss howyouwouldexpectequilibriumquantity andpriceto change.

1. Derivatives: Determine the derivatives of y with respect to x for each of the following functions. No need to simplify beyond the most straight-forward combining of like terms:

a. = 3 + 10 + 32 + 31/3

b. = 2(4 3) (Hint: Distribute the 2 before taking the derivative)

c. = (42)(22 3)

2. Optimization: Find the value of the decision variable, , that maximizes the objective function, , if = /22