Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK's demand for bricks is. The research department has estimated that ConstrUK's preferences over bricks (x) and cement (y) can be described by the utility function U(x,y) xb/10 y1-b/10 , where b=8, and where x and y are measured in bags. Example: if b=4, then U(x,y) = x+/10 y1-4/10 = x²/5 y3/ 5 %3D %3D The price for one bag of cement is equal to £1. It is estimated that ConstrUK's budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.

When trying to assess differences in her customers, Claire—the owner of Claire’s Rose Boutique—noticed a difference between the typical demand of her female versus her male customers. In particular, she found her female customers to be more price sensitive in general. After conducting some sales analysis, she determined that her female customers have the following demand curve for roses: QF = 24 − 2P. Here, QF is the quantity of roses demanded by a female customer and P is the price charged per rose. She determined that her male customers have the following demand curve for roses: QM = 27 − P. Here, QM is the quantity of roses demanded by a male customer. If two unaffiliated customers walk into her boutique, one male and one female, determine the demand curve for these two customers combined (i.e., what is their aggregate demand?).

A consumer has the following utility function U (X1, X2) = (x1 + 3) (x2+4) Prices of the two goods X₁ and x₂ respectively are p₁ and p2 and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m is high enough so that both goods are consumed in strictly positive amount in equilibrium. (a) Solve the consumer's optimization problem and express the demand for the two goods in terms of prices and income. (1) Compute the missing values of elasticities in the following table assuming M = 10, p₁ = 2, and p2 = 1. Show your work. Income elasticity Absolute value of own price elasticity Cross price elasticity X₁ T≤ X₂ (b) While x2 is produced locally, x₁ is transported from a different region. Assume P₂ = 1. Building a new railroad (that connects the regions) will reduce transportation cost which in turn will reduce the price of good 1 from p₁ = 2 to p₁ = 1. Railroad will be funded by taxes which will reduce…

Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials  I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.