The video game studio DreamSoft creates games for different consoles in London. The Playstation unit produces video games with a production function equal to qP(K,L)=K0.5L0.5where K is capital (say computers, cloud systems, etc.) and L is the number of developers. The mobile games unit produces video games with a production function equal toqM(K,L)=min{K,L}

1. Draw a few isoquants for these production functions.
2. Renting one unit of capital costs r = 100 thousand per year, and a developer costs w = 100 thousand per year. Write down the equation of the isocost function. Draw a diagram of it, assuming total costs and factor prices are calculated in thousands of pounds (i.e. 100 thousand pounds are a cost of 100).
3. The target for this year is to produce 10 new games for both platforms (10 for Playstation, 10 for mobile). Explain how DreamSoft should choose the optimal level of inputs, using equations and diagrams as needed.
4. DreamSoft discovers that developers cost much less in Barcelona, Spain. In fact, a developer costs only 16 thousand per year. It is, therefore, considering moving its operations to Barcelona, possibly only partially. Assume moving to Barcelona has no additional costs, and that DreamSoft still wants to produce 10 games for Playstation and 10 games for mobile gadgets. Which units, if any, should DreamSoft move to Barcelona?
5. How would your answer change if there were a one-off cost of moving to Barcelona equal to 1 million? Explain.